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Volumen 37 (2017): Edición 1 (June 2017)

Detalles de la revista
Formato
Revista
eISSN
2084-0373
Publicado por primera vez
16 Apr 2017
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

Volumen 40 (2020): Edición 2 (December 2020)

Detalles de la revista
Formato
Revista
eISSN
2084-0373
Publicado por primera vez
16 Apr 2017
Periodo de publicación
2 veces al año
Idiomas
Inglés

Buscar

14 Artículos
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 143 - 157

Resumen

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).

Palabras clave

  • graph algebra
  • groupoid
  • identities
  • semimediality
  • mediality

MSC 2010

  • 05C25
  • 03C05
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 159 - 164

Resumen

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.

Palabras clave

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

MSC 2010

  • 17B30
  • 17B60
  • 17B99
access type Acceso abierto

Commutativity with Derivations of Semiprime Rings

Publicado en línea: 20 Oct 2020
Páginas: 165 - 175

Resumen

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.

Palabras clave

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

MSC 2010

  • 16W25
  • 16N60
  • 16U80
access type Acceso abierto

Near Rings Characterized By Intuitionistic Fuzzy Bi Ideals

Publicado en línea: 20 Oct 2020
Páginas: 177 - 186

Resumen

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.

Palabras clave

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

MSC 2010

  • 16D25
  • 03E72
  • 03F55
  • 16Y30
access type Acceso abierto

A Note on Generalized Hybrid Tribonacci Numbers

Publicado en línea: 20 Oct 2020
Páginas: 187 - 199

Resumen

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.

Palabras clave

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

MSC 2010

  • Primary: 11B37
  • Secondary: 11B39, 97F50
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 201 - 216

Resumen

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.

Palabras clave

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

MSC 2010

  • 11B37
  • 11B39
access type Acceso abierto

The Cayley Sum Graph of Ideals of a Lattice

Publicado en línea: 20 Oct 2020
Páginas: 217 - 230

Resumen

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.

Palabras clave

  • lattice
  • Cayley graph
  • ring graph
  • outerplanar graph

MSC 2010

  • 05C69
  • 05C75
  • 06B10
access type Acceso abierto

Characterization of Almost Semi-Heyting Algebra

Publicado en línea: 20 Oct 2020
Páginas: 231 - 243

Resumen

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.

Palabras clave

  • 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 Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 245 - 265

Resumen

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.

Palabras clave

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

MSC 2010

  • Primary 05E05
  • Secondary 11B39
access type Acceso abierto

Isomorphisms in EQ-Algebras

Publicado en línea: 20 Oct 2020
Páginas: 267 - 274

Resumen

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.

Palabras clave

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

MSC 2010

  • 03B15
  • 08A72
access type Acceso abierto

Sums of Powers and Special Polynomials

Publicado en línea: 20 Oct 2020
Páginas: 275 - 283

Resumen

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.

Palabras clave

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

MSC 2010

  • 11B68
  • 11B73
  • 11C08
access type Acceso abierto

Completely Prime Hyperideals of Ternary Semihypergroups

Publicado en línea: 20 Oct 2020
Páginas: 285 - 295

Resumen

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.

Palabras clave

  • pseudosymmetric
  • globally idempotent
  • leftsimple ternary semi-hypergroup

MSC 2010

  • 20N20
  • 20M12
access type Acceso abierto

r-Ideals and m-k-Ideals in Inclines

Publicado en línea: 20 Oct 2020
Páginas: 297 - 309

Resumen

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.

Palabras clave

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

MSC 2010

  • 16A09
  • 06F25
access type Acceso abierto

β-Prime Spectrum of Stone Almost Distributive Lattices

Publicado en línea: 20 Oct 2020
Páginas: 311 - 326

Resumen

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.

Palabras clave

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

MSC 2010

  • 06D99
  • 06D15
14 Artículos
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 143 - 157

Resumen

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).

Palabras clave

  • graph algebra
  • groupoid
  • identities
  • semimediality
  • mediality

MSC 2010

  • 05C25
  • 03C05
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 159 - 164

Resumen

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.

Palabras clave

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

MSC 2010

  • 17B30
  • 17B60
  • 17B99
access type Acceso abierto

Commutativity with Derivations of Semiprime Rings

Publicado en línea: 20 Oct 2020
Páginas: 165 - 175

Resumen

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.

Palabras clave

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

MSC 2010

  • 16W25
  • 16N60
  • 16U80
access type Acceso abierto

Near Rings Characterized By Intuitionistic Fuzzy Bi Ideals

Publicado en línea: 20 Oct 2020
Páginas: 177 - 186

Resumen

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.

Palabras clave

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

MSC 2010

  • 16D25
  • 03E72
  • 03F55
  • 16Y30
access type Acceso abierto

A Note on Generalized Hybrid Tribonacci Numbers

Publicado en línea: 20 Oct 2020
Páginas: 187 - 199

Resumen

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.

Palabras clave

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

MSC 2010

  • Primary: 11B37
  • Secondary: 11B39, 97F50
access type Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 201 - 216

Resumen

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.

Palabras clave

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

MSC 2010

  • 11B37
  • 11B39
access type Acceso abierto

The Cayley Sum Graph of Ideals of a Lattice

Publicado en línea: 20 Oct 2020
Páginas: 217 - 230

Resumen

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.

Palabras clave

  • lattice
  • Cayley graph
  • ring graph
  • outerplanar graph

MSC 2010

  • 05C69
  • 05C75
  • 06B10
access type Acceso abierto

Characterization of Almost Semi-Heyting Algebra

Publicado en línea: 20 Oct 2020
Páginas: 231 - 243

Resumen

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.

Palabras clave

  • 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 Acceso abierto

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

Publicado en línea: 20 Oct 2020
Páginas: 245 - 265

Resumen

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.

Palabras clave

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

MSC 2010

  • Primary 05E05
  • Secondary 11B39
access type Acceso abierto

Isomorphisms in EQ-Algebras

Publicado en línea: 20 Oct 2020
Páginas: 267 - 274

Resumen

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.

Palabras clave

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

MSC 2010

  • 03B15
  • 08A72
access type Acceso abierto

Sums of Powers and Special Polynomials

Publicado en línea: 20 Oct 2020
Páginas: 275 - 283

Resumen

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.

Palabras clave

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

MSC 2010

  • 11B68
  • 11B73
  • 11C08
access type Acceso abierto

Completely Prime Hyperideals of Ternary Semihypergroups

Publicado en línea: 20 Oct 2020
Páginas: 285 - 295

Resumen

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.

Palabras clave

  • pseudosymmetric
  • globally idempotent
  • leftsimple ternary semi-hypergroup

MSC 2010

  • 20N20
  • 20M12
access type Acceso abierto

r-Ideals and m-k-Ideals in Inclines

Publicado en línea: 20 Oct 2020
Páginas: 297 - 309

Resumen

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.

Palabras clave

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

MSC 2010

  • 16A09
  • 06F25
access type Acceso abierto

β-Prime Spectrum of Stone Almost Distributive Lattices

Publicado en línea: 20 Oct 2020
Páginas: 311 - 326

Resumen

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.

Palabras clave

  • 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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