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Informacje o czasopiśmie
Format
Czasopismo
eISSN
2084-0373
Pierwsze wydanie
16 Apr 2017
Częstotliwość wydawania
2 razy w roku
Języki
Angielski

Wyszukiwanie

Tom 40 (2020): Zeszyt 2 (December 2020)

Informacje o czasopiśmie
Format
Czasopismo
eISSN
2084-0373
Pierwsze wydanie
16 Apr 2017
Częstotliwość wydawania
2 razy w roku
Języki
Angielski

Wyszukiwanie

14 Artykułów
access type Otwarty dostęp

Graph Varieties Axiomatized by Semimedial, Medial, and Some Other Groupoid Identities

Data publikacji: 20 Oct 2020
Zakres stron: 143 - 157

Abstrakt

Abstract

Directed graphs without multiple edges can be represented as algebras of type (2, 0), so-called graph algebras. A graph is said to satisfy an identity if the corresponding graph algebra does, and the set of all graphs satisfying a set of identities is called a graph variety. We describe the graph varieties axiomatized by certain groupoid identities (medial, semimedial, autodistributive, commutative, idempotent, unipotent, zeropotent, alternative).

Słowa kluczowe

  • graph algebra
  • groupoid
  • identities
  • semimediality
  • mediality

MSC 2010

  • 05C25
  • 03C05
access type Otwarty dostęp

Some Upper Bounds for the Dimension of the c-Nilpotent Multiplier of a Pair of Lie Algebras

Data publikacji: 20 Oct 2020
Zakres stron: 159 - 164

Abstrakt

Abstract

The notion of the Schur multiplier of a Lie algebra L was introduced by Batten in 1996. Recently, the first author introduced the concept of the cnilpotent multiplier of a pair of Lie algebras and gave some exact sequences for the c-nilpotent multiplier of a pair of Lie algebras. The purpose of this paper is to derive some inequalities for dimension of the c-nilpotent multiplier of a pair of Lie algebras.

Słowa kluczowe

  • pair of Lie algebras
  • Schur multiplier
  • nilpotent Lie algebra

MSC 2010

  • 17B30
  • 17B60
  • 17B99
access type Otwarty dostęp

Commutativity with Derivations of Semiprime Rings

Data publikacji: 20 Oct 2020
Zakres stron: 165 - 175

Abstrakt

Abstract

Let R be a 2-torsion free semiprime ring with the centre Z(R), U be a non-zero ideal and d: RR be a derivation mapping. Suppose that R admits

(1) a derivation d satisfying one of the following conditions:

(i) [d(x), d(y)] − [x, y] ∈ Z(R) for all x, yU,

(ii) [d2(x), d2(y)] − [x, y] ∈ Z(R) for all x, yU,

(iii) [d(x)2, d(y)2] − [x, y] ∈ Z(R) for all x, yU,

(iv) [d(x2), d(y2)] − [x, y] ∈ Z(R) for all x, yU,

(v) [d(x), d(y)] − [x2, y2] ∈ Z(R) for all x, yU.

(2) a non-zero derivation d satisfying one of the following conditions:

(i) d([d(x), d(y)]) − [x, y] ∈ Z(R) for all x, yU,

(ii) d([d(x), d(y)]) + [x, y] ∈ Z(R) for all x, yU.

Then R contains a non-zero central ideal.

Słowa kluczowe

  • semiprime rings
  • derivations
  • torsion free rings
  • central ideal

MSC 2010

  • 16W25
  • 16N60
  • 16U80
access type Otwarty dostęp

Near Rings Characterized By Intuitionistic Fuzzy Bi Ideals

Data publikacji: 20 Oct 2020
Zakres stron: 177 - 186

Abstrakt

Abstract

Generalizing the concept of fuzzy bi ideals of near rings, the notion of intuitionistic fuzzy bi ideals of near rings is introduced. We also characterize and investigate some related properties of intuitionistic fuzzy bi ideals of near rings.

Słowa kluczowe

  • near rings
  • fuzzy bi ideals
  • intuitionistic fuzzy subnear ring
  • intuitionistic fuzzy ideals
  • intuitionistic fuzzy bi ideals

MSC 2010

  • 16D25
  • 03E72
  • 03F55
  • 16Y30
access type Otwarty dostęp

A Note on Generalized Hybrid Tribonacci Numbers

Data publikacji: 20 Oct 2020
Zakres stron: 187 - 199

Abstrakt

Abstract

In this paper, we introduce the generalized hybrid Tribonacci numbers. These numbers can be considered as a generalization of the generalized complex Tribonacci, generalized hyperbolic Tribonacci and generalized dual Tribonacci numbers. We also obtain some identities for these numbers.

Słowa kluczowe

  • complex numbers
  • hyperbolic numbers
  • dual numbers
  • hybrid numbers
  • generalized Tribonacci numbers

MSC 2010

  • Primary: 11B37
  • Secondary: 11B39, 97F50
access type Otwarty dostęp

On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers

Data publikacji: 20 Oct 2020
Zakres stron: 201 - 216

Abstrakt

Abstract

In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.

Słowa kluczowe

  • balancing numbers
  • Lucas-balancing numbers
  • partial sums
  • reciprocal
  • floor function

MSC 2010

  • 11B37
  • 11B39
access type Otwarty dostęp

The Cayley Sum Graph of Ideals of a Lattice

Data publikacji: 20 Oct 2020
Zakres stron: 217 - 230

Abstrakt

Abstract

Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that IK = J or JK = I. We study some basic properties of the graph ΓL,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓL,S.

Słowa kluczowe

  • lattice
  • Cayley graph
  • ring graph
  • outerplanar graph

MSC 2010

  • 05C69
  • 05C75
  • 06B10
access type Otwarty dostęp

Characterization of Almost Semi-Heyting Algebra

Data publikacji: 20 Oct 2020
Zakres stron: 231 - 243

Abstrakt

Abstract

In this paper, we initiate the discourse on the properties that hold in an almost semi-Heyting algebra but not in an semi-Heyting almost distributive lattice. We establish an equivalent condition for an almost semi-Heyting algebra to become a Stone almost distributive lattice. Moreover a glance about dense elements in an almost semi-Heyting algebra followed by study of some algebraic properties on them. Finally, we perceive that the kernel of homomorphism is equal to the dense element set.

Słowa kluczowe

  • almost distributive lattice
  • semi-Heyting almost distributive lattice
  • almost semi-Heyting algebra
  • dense element and stone almost distributive lattice

MSC 2010

  • Primary 06D99
  • Secondary 06D20
access type Otwarty dostęp

Generating Functions of the Products of Bivariate Complex Fibonacci Polynomials with Gaussian Numbers and Polynomials

Data publikacji: 20 Oct 2020
Zakres stron: 245 - 265

Abstrakt

Abstract

In this paper, we define and study the bivariate complex Fibonacci and Lucas polynomials. We introduce a operator in order to derive some new symmetric properties of bivariate complex Fibonacci and bivariate complex Lucas polynomials, and give the generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Fibonacci, Gaussian Lucas and Gaussian Jacobsthal numbers, Gaussian Pell numbers, Gaussian Pell Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Jacobsthal, Gaussian Jacobsthal Lucas polynomials and Gaussian Pell polynomials.

Słowa kluczowe

  • symmetric functions
  • generating functions
  • bivariate complex Fibonacci polynomials
  • bivariate complex Lucas polynomials

MSC 2010

  • Primary 05E05
  • Secondary 11B39
access type Otwarty dostęp

Isomorphisms in EQ-Algebras

Data publikacji: 20 Oct 2020
Zakres stron: 267 - 274

Abstrakt

Abstract

In this paper we investigate some isomorphism theorems in EQ-algebras. After establishing some basic results we give the Fundamental Homomorphism Theorem and by using it we state and prove some other isomorphism theorems. We also state and prove a correspondence theorem. Next, using some results of the theory of universal algebra we characterize subdirectly irreducible EQ-algebras.

Słowa kluczowe

  • many-valued logics
  • Fuzzy type theory
  • EQ-algebra
  • homomorphism theorems

MSC 2010

  • 03B15
  • 08A72
access type Otwarty dostęp

Sums of Powers and Special Polynomials

Data publikacji: 20 Oct 2020
Zakres stron: 275 - 283

Abstrakt

Abstract

In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their connection to other interesting series. In particular, we show their connection to an interesting problem of Ovidiu Furdui.

Słowa kluczowe

  • sum of powers
  • exponential polynomial
  • geometric polynomial
  • generating function
  • harmonic numbers
  • exponential integral function

MSC 2010

  • 11B68
  • 11B73
  • 11C08
access type Otwarty dostęp

Completely Prime Hyperideals of Ternary Semihypergroups

Data publikacji: 20 Oct 2020
Zakres stron: 285 - 295

Abstrakt

Abstract

In this article, we introduce the notions of pseudosymmetric hyperideals and globally idempotent ternary semihypergroups and present various examples for them. We prove that if a ternary semihypergroup is globally idempotent, then every maximal hyperideal is a prime hyperideal. Also we study some properties of prime, completely prime and pseudosymmetric hyperideals of a ternary semihypergroup and characterize them. The interrelation among them is considered in ternary semihypergroups.

Słowa kluczowe

  • pseudosymmetric
  • globally idempotent
  • leftsimple ternary semi-hypergroup

MSC 2010

  • 20N20
  • 20M12
access type Otwarty dostęp

r-Ideals and m-k-Ideals in Inclines

Data publikacji: 20 Oct 2020
Zakres stron: 297 - 309

Abstrakt

Abstract

In this paper, we introduce the notion of r-ideal and m-k-ideal in inclines. We study the properties of r-ideals and m-k-ideals, the relations between them and characterize m-k-ideal and r-ideal in inclines.

Słowa kluczowe

  • incline
  • integral incline
  • regular incline
  • mono incline
  • prime ideal
  • maximal ideal
  • -ideal
  • -ideal
  • --ideal

MSC 2010

  • 16A09
  • 06F25
access type Otwarty dostęp

β-Prime Spectrum of Stone Almost Distributive Lattices

Data publikacji: 20 Oct 2020
Zakres stron: 311 - 326

Abstrakt

Abstract

The notion of boosters and β-filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the β-filters. It has been derived that every proper β-filter is the intersection of all prime β-filters containing it, and it has also been proved that the set 𝒡β (L) of all β-filters is isomorphic to the set of all ideals of 𝒝0(L). A set of equivalent conditions is derived for 𝒝0(L) to become a relatively complemented Almost Distributive Lattice. Later, some properties of the space of all prime β-filters are derived topologically. Finally, necessary and sufficient conditions are derived for the space of all prime β-filters to be a Hausdorff space.

Słowa kluczowe

  • Almost Distributive Lattice (ADL)
  • stone ADL
  • relatively complemented ADL
  • ideal
  • filter
  • booster
  • -filters
  • isomorphism
  • compact set
  • Hausdorff space

MSC 2010

  • 06D99
  • 06D15
14 Artykułów
access type Otwarty dostęp

Graph Varieties Axiomatized by Semimedial, Medial, and Some Other Groupoid Identities

Data publikacji: 20 Oct 2020
Zakres stron: 143 - 157

Abstrakt

Abstract

Directed graphs without multiple edges can be represented as algebras of type (2, 0), so-called graph algebras. A graph is said to satisfy an identity if the corresponding graph algebra does, and the set of all graphs satisfying a set of identities is called a graph variety. We describe the graph varieties axiomatized by certain groupoid identities (medial, semimedial, autodistributive, commutative, idempotent, unipotent, zeropotent, alternative).

Słowa kluczowe

  • graph algebra
  • groupoid
  • identities
  • semimediality
  • mediality

MSC 2010

  • 05C25
  • 03C05
access type Otwarty dostęp

Some Upper Bounds for the Dimension of the c-Nilpotent Multiplier of a Pair of Lie Algebras

Data publikacji: 20 Oct 2020
Zakres stron: 159 - 164

Abstrakt

Abstract

The notion of the Schur multiplier of a Lie algebra L was introduced by Batten in 1996. Recently, the first author introduced the concept of the cnilpotent multiplier of a pair of Lie algebras and gave some exact sequences for the c-nilpotent multiplier of a pair of Lie algebras. The purpose of this paper is to derive some inequalities for dimension of the c-nilpotent multiplier of a pair of Lie algebras.

Słowa kluczowe

  • pair of Lie algebras
  • Schur multiplier
  • nilpotent Lie algebra

MSC 2010

  • 17B30
  • 17B60
  • 17B99
access type Otwarty dostęp

Commutativity with Derivations of Semiprime Rings

Data publikacji: 20 Oct 2020
Zakres stron: 165 - 175

Abstrakt

Abstract

Let R be a 2-torsion free semiprime ring with the centre Z(R), U be a non-zero ideal and d: RR be a derivation mapping. Suppose that R admits

(1) a derivation d satisfying one of the following conditions:

(i) [d(x), d(y)] − [x, y] ∈ Z(R) for all x, yU,

(ii) [d2(x), d2(y)] − [x, y] ∈ Z(R) for all x, yU,

(iii) [d(x)2, d(y)2] − [x, y] ∈ Z(R) for all x, yU,

(iv) [d(x2), d(y2)] − [x, y] ∈ Z(R) for all x, yU,

(v) [d(x), d(y)] − [x2, y2] ∈ Z(R) for all x, yU.

(2) a non-zero derivation d satisfying one of the following conditions:

(i) d([d(x), d(y)]) − [x, y] ∈ Z(R) for all x, yU,

(ii) d([d(x), d(y)]) + [x, y] ∈ Z(R) for all x, yU.

Then R contains a non-zero central ideal.

Słowa kluczowe

  • semiprime rings
  • derivations
  • torsion free rings
  • central ideal

MSC 2010

  • 16W25
  • 16N60
  • 16U80
access type Otwarty dostęp

Near Rings Characterized By Intuitionistic Fuzzy Bi Ideals

Data publikacji: 20 Oct 2020
Zakres stron: 177 - 186

Abstrakt

Abstract

Generalizing the concept of fuzzy bi ideals of near rings, the notion of intuitionistic fuzzy bi ideals of near rings is introduced. We also characterize and investigate some related properties of intuitionistic fuzzy bi ideals of near rings.

Słowa kluczowe

  • near rings
  • fuzzy bi ideals
  • intuitionistic fuzzy subnear ring
  • intuitionistic fuzzy ideals
  • intuitionistic fuzzy bi ideals

MSC 2010

  • 16D25
  • 03E72
  • 03F55
  • 16Y30
access type Otwarty dostęp

A Note on Generalized Hybrid Tribonacci Numbers

Data publikacji: 20 Oct 2020
Zakres stron: 187 - 199

Abstrakt

Abstract

In this paper, we introduce the generalized hybrid Tribonacci numbers. These numbers can be considered as a generalization of the generalized complex Tribonacci, generalized hyperbolic Tribonacci and generalized dual Tribonacci numbers. We also obtain some identities for these numbers.

Słowa kluczowe

  • complex numbers
  • hyperbolic numbers
  • dual numbers
  • hybrid numbers
  • generalized Tribonacci numbers

MSC 2010

  • Primary: 11B37
  • Secondary: 11B39, 97F50
access type Otwarty dostęp

On the Partial Finite Alternating Sums of Reciprocals of Balancing and Lucas-Balancing Numbers

Data publikacji: 20 Oct 2020
Zakres stron: 201 - 216

Abstrakt

Abstract

In this note, the finite alternating sums of reciprocals of balancing and Lucas-balancing numbers are considered and several identities involving these sums are deduced.

Słowa kluczowe

  • balancing numbers
  • Lucas-balancing numbers
  • partial sums
  • reciprocal
  • floor function

MSC 2010

  • 11B37
  • 11B39
access type Otwarty dostęp

The Cayley Sum Graph of Ideals of a Lattice

Data publikacji: 20 Oct 2020
Zakres stron: 217 - 230

Abstrakt

Abstract

Let L be a lattice, 𝒥(L) be the set of ideals of L and S be a subset of 𝒥 (L). In this paper, we introduce an undirected Cayley graph of L, denoted by ΓL,S with elements of 𝒥 (L) as the vertex set and, for two distinct vertices I and J, I is adjacent to J if and only if there is an element K of S such that IK = J or JK = I. We study some basic properties of the graph ΓL,S such as connectivity, girth and clique number. Moreover, we investigate the planarity, outerplanarity and ring graph of ΓL,S.

Słowa kluczowe

  • lattice
  • Cayley graph
  • ring graph
  • outerplanar graph

MSC 2010

  • 05C69
  • 05C75
  • 06B10
access type Otwarty dostęp

Characterization of Almost Semi-Heyting Algebra

Data publikacji: 20 Oct 2020
Zakres stron: 231 - 243

Abstrakt

Abstract

In this paper, we initiate the discourse on the properties that hold in an almost semi-Heyting algebra but not in an semi-Heyting almost distributive lattice. We establish an equivalent condition for an almost semi-Heyting algebra to become a Stone almost distributive lattice. Moreover a glance about dense elements in an almost semi-Heyting algebra followed by study of some algebraic properties on them. Finally, we perceive that the kernel of homomorphism is equal to the dense element set.

Słowa kluczowe

  • almost distributive lattice
  • semi-Heyting almost distributive lattice
  • almost semi-Heyting algebra
  • dense element and stone almost distributive lattice

MSC 2010

  • Primary 06D99
  • Secondary 06D20
access type Otwarty dostęp

Generating Functions of the Products of Bivariate Complex Fibonacci Polynomials with Gaussian Numbers and Polynomials

Data publikacji: 20 Oct 2020
Zakres stron: 245 - 265

Abstrakt

Abstract

In this paper, we define and study the bivariate complex Fibonacci and Lucas polynomials. We introduce a operator in order to derive some new symmetric properties of bivariate complex Fibonacci and bivariate complex Lucas polynomials, and give the generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Fibonacci, Gaussian Lucas and Gaussian Jacobsthal numbers, Gaussian Pell numbers, Gaussian Pell Lucas numbers. By making use of the operator defined in this paper, we give some new generating functions of the products of bivariate complex Fibonacci polynomials with Gaussian Jacobsthal, Gaussian Jacobsthal Lucas polynomials and Gaussian Pell polynomials.

Słowa kluczowe

  • symmetric functions
  • generating functions
  • bivariate complex Fibonacci polynomials
  • bivariate complex Lucas polynomials

MSC 2010

  • Primary 05E05
  • Secondary 11B39
access type Otwarty dostęp

Isomorphisms in EQ-Algebras

Data publikacji: 20 Oct 2020
Zakres stron: 267 - 274

Abstrakt

Abstract

In this paper we investigate some isomorphism theorems in EQ-algebras. After establishing some basic results we give the Fundamental Homomorphism Theorem and by using it we state and prove some other isomorphism theorems. We also state and prove a correspondence theorem. Next, using some results of the theory of universal algebra we characterize subdirectly irreducible EQ-algebras.

Słowa kluczowe

  • many-valued logics
  • Fuzzy type theory
  • EQ-algebra
  • homomorphism theorems

MSC 2010

  • 03B15
  • 08A72
access type Otwarty dostęp

Sums of Powers and Special Polynomials

Data publikacji: 20 Oct 2020
Zakres stron: 275 - 283

Abstrakt

Abstract

In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their connection to other interesting series. In particular, we show their connection to an interesting problem of Ovidiu Furdui.

Słowa kluczowe

  • sum of powers
  • exponential polynomial
  • geometric polynomial
  • generating function
  • harmonic numbers
  • exponential integral function

MSC 2010

  • 11B68
  • 11B73
  • 11C08
access type Otwarty dostęp

Completely Prime Hyperideals of Ternary Semihypergroups

Data publikacji: 20 Oct 2020
Zakres stron: 285 - 295

Abstrakt

Abstract

In this article, we introduce the notions of pseudosymmetric hyperideals and globally idempotent ternary semihypergroups and present various examples for them. We prove that if a ternary semihypergroup is globally idempotent, then every maximal hyperideal is a prime hyperideal. Also we study some properties of prime, completely prime and pseudosymmetric hyperideals of a ternary semihypergroup and characterize them. The interrelation among them is considered in ternary semihypergroups.

Słowa kluczowe

  • pseudosymmetric
  • globally idempotent
  • leftsimple ternary semi-hypergroup

MSC 2010

  • 20N20
  • 20M12
access type Otwarty dostęp

r-Ideals and m-k-Ideals in Inclines

Data publikacji: 20 Oct 2020
Zakres stron: 297 - 309

Abstrakt

Abstract

In this paper, we introduce the notion of r-ideal and m-k-ideal in inclines. We study the properties of r-ideals and m-k-ideals, the relations between them and characterize m-k-ideal and r-ideal in inclines.

Słowa kluczowe

  • incline
  • integral incline
  • regular incline
  • mono incline
  • prime ideal
  • maximal ideal
  • -ideal
  • -ideal
  • --ideal

MSC 2010

  • 16A09
  • 06F25
access type Otwarty dostęp

β-Prime Spectrum of Stone Almost Distributive Lattices

Data publikacji: 20 Oct 2020
Zakres stron: 311 - 326

Abstrakt

Abstract

The notion of boosters and β-filters in stone Almost Distributive Lattices are introduced and their properties are studied, utilizing boosters to characterize the β-filters. It has been derived that every proper β-filter is the intersection of all prime β-filters containing it, and it has also been proved that the set 𝒡β (L) of all β-filters is isomorphic to the set of all ideals of 𝒝0(L). A set of equivalent conditions is derived for 𝒝0(L) to become a relatively complemented Almost Distributive Lattice. Later, some properties of the space of all prime β-filters are derived topologically. Finally, necessary and sufficient conditions are derived for the space of all prime β-filters to be a Hausdorff space.

Słowa kluczowe

  • Almost Distributive Lattice (ADL)
  • stone ADL
  • relatively complemented ADL
  • ideal
  • filter
  • booster
  • -filters
  • isomorphism
  • compact set
  • Hausdorff space

MSC 2010

  • 06D99
  • 06D15

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