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Volume 42 (2022): Edition 1 (March 2022)

Volume 41 (2021): Edition 2 (November 2021)

Volume 41 (2021): Edition 1 (May 2021)

Volume 40 (2020): Edition 2 (December 2020)

Volume 40 (2020): Edition 1 (June 2020)

Volume 39 (2019): Edition 2 (December 2019)

Volume 39 (2019): Edition 1 (June 2019)

Volume 38 (2018): Edition 2 (December 2018)

Volume 38 (2018): Edition 1 (June 2018)

Volume 37 (2017): Edition 2 (December 2017)

Volume 37 (2017): Edition 1 (June 2017)

Détails du magazine
Format
Magazine
eISSN
2084-0373
Première publication
16 Apr 2017
Période de publication
2 fois par an
Langues
Anglais

Chercher

Volume 42 (2022): Edition 1 (March 2022)

Détails du magazine
Format
Magazine
eISSN
2084-0373
Première publication
16 Apr 2017
Période de publication
2 fois par an
Langues
Anglais

Chercher

11 Articles
Accès libre

Generalized Centroid of Hyperrings

Publié en ligne: 05 Apr 2022
Pages: 5 - 16

Résumé

Abstract

In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid C of a semiprime hyperring R is a regular hyperring. Also, we show that if C is a hyperfield, then R is a prime hyperring.

Mots clés

  • hyperring
  • semiprime hyperring
  • generalized centroid
  • regular hyperring

MSC 2010

  • 20N20
  • 16Y20
Accès libre

Hyper Rl-Ideals in Hyper Residuated Lattices

Publié en ligne: 05 Apr 2022
Pages: 17 - 29

Résumé

Abstract

In this paper, we introduce the notion of a (strong) hyper RL-ideal in hyper residuated lattices and give some properties and characterizations of them. Next, we characterize the (strong) hyper RL-ideals generated by a subset and give some characterizations of the lattice of these hyper RL-ideals. Particularly, we prove that this lattice is algebraic and compact elements are finitely generated hyper RL-ideals, and obtain some isomorphism theorems. Finally, we introduce the notion of nodal hyper RL-ideals in a hyper residuated lattice and investigate their properties. We prove that the set of nodal hyper RL-ideals is a complete Brouwerian lattice and under suitable operations is a Heyting algebra.

Mots clés

  • residuated lattice
  • MV-algebra
  • BL-algebra
  • hyper residuated lattice
  • hyper ideal

MSC 2010

  • 03B50
  • 06D35
  • 03E72
Accès libre

New Kinds of Prefilters in EQ-Algebras

Publié en ligne: 05 Apr 2022
Pages: 31 - 49

Résumé

Abstract

In this paper, the notions of n-fold positive implicative prefilter and n-fold implicative prefilter in EQ-algebras are introduced and several properties, characterizations and equivalent conditions are provided. It is proved that the quotient EQ-algebra induced by an n-fold positive implicative prefilter is n-idempotent. Also, it is proved that in an n-idempotent EQ-algebra, any filter is an n-fold positive implicative filter. In the sequel, we investigate the relationships between these two types of prefilters. Finally, some characterizations of n-fold implicative prefilters in bounded EQ-algebras are given.

Mots clés

  • (-idempotent) EQ-algebra
  • -fold positive implicative prefilter
  • -fold implicative prefilter

MSC 2010

  • 03G25
  • 06F35
Accès libre

Stone Commutator Lattices and Baer Rings

Publié en ligne: 05 Apr 2022
Pages: 51 - 96

Résumé

Abstract

In this paper, we transfer Davey‘s characterization for κ -Stone bounded distributive lattices to lattices with certain kinds of quotients, in particular to commutator lattices with certain properties, and obtain related results on prime, radical, complemented and compact elements, annihilators and congruences of these lattices. We then apply these results to certain congruence lattices, in particular to those of semiprime members of semi-degenerate congruence-modular varieties, and use this particular case to transfer Davey‘s Theorem to commutative unitary rings.

Mots clés

  • (strongly) Stone lattice
  • commutator lattice
  • annihilator
  • modular commutator
  • Baer ring

MSC 2010

  • Primary: 06B10
  • Secondary: 06D22, 08A30, 08B10
Accès libre

Prime Ideals of Transitive BE-Algebras

Publié en ligne: 05 Apr 2022
Pages: 97 - 119

Résumé

Abstract

The notion of prime ideals is introduced in transitive BE-algebras. Prime ideals are characterized with the help of principal ideals. Prime ideal theorem is stated and derived for BE-algebras. The concept of minimal prime ideals is introduced in transitive BE-algebras. A decomposition theorem of proper ideals into minimal prime ideals is derived.

Mots clés

  • transitive -algebra
  • ideal
  • maximal ideal
  • prime ideal

MSC 2010

  • 03G25
Accès libre

On the Structure Space of a Г -Semigroup Via Its Left Operator Semigroup

Publié en ligne: 05 Apr 2022
Pages: 121 - 134

Résumé

Abstract

The structure space of a semigroup endowed with hull kernel topology is introduced and studied. Also the structure space of a Г -semigroup is defined and a homeomorphism has been established between structure space of a Г -semigroup and the structure space of its left operator semigroup. Moreover, various properties of structure space of a Г -semigroup are studied via its left operator semigroup.

Mots clés

  • operator semigroup
  • Г -semigroup
  • prime ideal
  • hull-kernel topology

MSC 2010

  • 20M12
  • 20Mxx
Accès libre

Order of Finite Soft Quasigroups with Application to Egalitarianism

Publié en ligne: 05 Apr 2022
Pages: 135 - 157

Résumé

Abstract

In this work, a soft set (F, A) was introduced over a quasigroup (Q,) and the study of finite soft quasigroup was carried out, motivated by the study of algebraic structures of soft sets. By introducing the order of a finite soft quasigroup, various inequality relationships that exist between the order of a finite quasigroup, the order of its soft quasigroup and the cardinality of its set of parameters were established. By introducing the arithmetic mean 𝒜ℱ(F, A) and geometric mean 𝒢ℱ(F, A) of a finite soft quasigroup (F, A), a sort of Lagrange’s Formula |(F, A)| = |A|𝒜ℱ(F, A) for finite soft quasigroup was gotten. Some of the inequalities gotten gave an upper bound for the order of a finite soft quasigroup in terms of the order of its quasigroup and cardinality of its set of parameters, and a lower bound for the order of the quasigroup in terms of the arithmetic mean of the finite soft quasigroup. A chain of inequalities called the Maclaurin’s inequality for any finite soft quasigroup (F, A)(Q,·) was shown to exist. A necessary and sufficient condition for a type of finite soft quasigroup to be extensible to a finite super soft quasigroup was established. This result is of practical use whenever a larger set of parameters is required. The results therein were illustrated with examples. Application to uniformity, equality and equity in distribution for social living is considered.

Mots clés

  • soft sets
  • quasigroups
  • soft quasigroups
  • soft subquasigroups
  • arithmetic and geometric mean
  • inequalities

MSC 2010

  • Primary 20N05, 03E72
  • Secondary 03E75
Accès libre

Disjunctive Ideals of Almost Distributive Lattices

Publié en ligne: 05 Apr 2022
Pages: 159 - 178

Résumé

Abstract

The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.

Mots clés

  • Almost Distributive Lattice (ADL)
  • normal ADL
  • disjunctive ideal
  • strongly disjunctive ideal
  • normal prime ideal
  • minimal prime ideal

MSC 2010

  • 06D99
  • 06D15
Accès libre

Fuzzy Distributive Pairs in Fuzzy Lattices

Publié en ligne: 05 Apr 2022
Pages: 179 - 199

Résumé

Abstract

We generalize the concept of a fuzzy distributive lattice by introducing the concepts of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair in a fuzzy lattice. A relationship among a fuzzy join-distributive pair, a fuzzy join-semidistributive pair and a fuzzy join-modular pair is proved. It is shown that for a pair of fuzzy atoms, the notions of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair coincide.

Mots clés

  • fuzzy lattices
  • fuzzy modular pair
  • fuzzy distributive pair
  • fuzzy semi-distributive pair

MSC 2010

  • 03B52
  • 03E72
  • 06D72
  • 06D99
Accès libre

Study of Additively Regular Г -Semirings and Derivations

Publié en ligne: 05 Apr 2022
Pages: 201 - 215

Résumé

Abstract

In this paper, the notions of commutator and derivation in additively regular -semirings with (A2, Г)-condition are introduced. We also characterize Jordan product for additively regular Г -semiring and establish some results which investigate the relationship between commutators, derivations and inner derivations. In 1957, E.C. Posner has shown that if there exists a non-zero centralizing derivation in a prime ring R, then R is commutative. This result is extended in the frame work of derivations of prime additively regular Г -semirings.

Mots clés

  • semirings
  • Г -semirings
  • additively regular Г -semirings
  • derivations and commutators

MSC 2010

  • 16Y60
  • 16Y99
Accès libre

Interior GE-Filters of GE-Algebras

Publié en ligne: 05 Apr 2022
Pages: 217 - 235

Résumé

Abstract

The notions of an interior GE-filter, a weak interior GE-filter and a belligerent interior GE-filter are introduced, and their relations and properties are investigated. Example of a GE-filter which is neither an interior GE-filter nor a weak interior GE-filter is provided. Relations between a weak interior GE-filter and an interior GE-filter are discussed, and conditions under which every weak interior GE-filter is an interior GE-filter are investigated. Relations between a belligerent interior GE-filter and an interior GE-filter are displayed, and conditions for an interior GE-filter to be a belligerent interior GE-filter are considered. Given a subset and an element, an interior GE-filter is established, and conditions for a subset to be a belligerent interior GE-filter are discussed. The extensibility of the beligerant interior GE-filter is debated. Relationships between weak interior GE-filter and belligerent interior GE-filter of type 1, type 2 and type 3 are founded.

Mots clés

  • (transitive, left exchangeable) GE-algebra
  • GE-filter
  • belligerent GE-filter
  • (weak) interior GE-filter
  • belligerent interior GE-filter (of type 1, type 2 and type 3)

MSC 2010

  • 03G25
  • 06F35
11 Articles
Accès libre

Generalized Centroid of Hyperrings

Publié en ligne: 05 Apr 2022
Pages: 5 - 16

Résumé

Abstract

In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid C of a semiprime hyperring R is a regular hyperring. Also, we show that if C is a hyperfield, then R is a prime hyperring.

Mots clés

  • hyperring
  • semiprime hyperring
  • generalized centroid
  • regular hyperring

MSC 2010

  • 20N20
  • 16Y20
Accès libre

Hyper Rl-Ideals in Hyper Residuated Lattices

Publié en ligne: 05 Apr 2022
Pages: 17 - 29

Résumé

Abstract

In this paper, we introduce the notion of a (strong) hyper RL-ideal in hyper residuated lattices and give some properties and characterizations of them. Next, we characterize the (strong) hyper RL-ideals generated by a subset and give some characterizations of the lattice of these hyper RL-ideals. Particularly, we prove that this lattice is algebraic and compact elements are finitely generated hyper RL-ideals, and obtain some isomorphism theorems. Finally, we introduce the notion of nodal hyper RL-ideals in a hyper residuated lattice and investigate their properties. We prove that the set of nodal hyper RL-ideals is a complete Brouwerian lattice and under suitable operations is a Heyting algebra.

Mots clés

  • residuated lattice
  • MV-algebra
  • BL-algebra
  • hyper residuated lattice
  • hyper ideal

MSC 2010

  • 03B50
  • 06D35
  • 03E72
Accès libre

New Kinds of Prefilters in EQ-Algebras

Publié en ligne: 05 Apr 2022
Pages: 31 - 49

Résumé

Abstract

In this paper, the notions of n-fold positive implicative prefilter and n-fold implicative prefilter in EQ-algebras are introduced and several properties, characterizations and equivalent conditions are provided. It is proved that the quotient EQ-algebra induced by an n-fold positive implicative prefilter is n-idempotent. Also, it is proved that in an n-idempotent EQ-algebra, any filter is an n-fold positive implicative filter. In the sequel, we investigate the relationships between these two types of prefilters. Finally, some characterizations of n-fold implicative prefilters in bounded EQ-algebras are given.

Mots clés

  • (-idempotent) EQ-algebra
  • -fold positive implicative prefilter
  • -fold implicative prefilter

MSC 2010

  • 03G25
  • 06F35
Accès libre

Stone Commutator Lattices and Baer Rings

Publié en ligne: 05 Apr 2022
Pages: 51 - 96

Résumé

Abstract

In this paper, we transfer Davey‘s characterization for κ -Stone bounded distributive lattices to lattices with certain kinds of quotients, in particular to commutator lattices with certain properties, and obtain related results on prime, radical, complemented and compact elements, annihilators and congruences of these lattices. We then apply these results to certain congruence lattices, in particular to those of semiprime members of semi-degenerate congruence-modular varieties, and use this particular case to transfer Davey‘s Theorem to commutative unitary rings.

Mots clés

  • (strongly) Stone lattice
  • commutator lattice
  • annihilator
  • modular commutator
  • Baer ring

MSC 2010

  • Primary: 06B10
  • Secondary: 06D22, 08A30, 08B10
Accès libre

Prime Ideals of Transitive BE-Algebras

Publié en ligne: 05 Apr 2022
Pages: 97 - 119

Résumé

Abstract

The notion of prime ideals is introduced in transitive BE-algebras. Prime ideals are characterized with the help of principal ideals. Prime ideal theorem is stated and derived for BE-algebras. The concept of minimal prime ideals is introduced in transitive BE-algebras. A decomposition theorem of proper ideals into minimal prime ideals is derived.

Mots clés

  • transitive -algebra
  • ideal
  • maximal ideal
  • prime ideal

MSC 2010

  • 03G25
Accès libre

On the Structure Space of a Г -Semigroup Via Its Left Operator Semigroup

Publié en ligne: 05 Apr 2022
Pages: 121 - 134

Résumé

Abstract

The structure space of a semigroup endowed with hull kernel topology is introduced and studied. Also the structure space of a Г -semigroup is defined and a homeomorphism has been established between structure space of a Г -semigroup and the structure space of its left operator semigroup. Moreover, various properties of structure space of a Г -semigroup are studied via its left operator semigroup.

Mots clés

  • operator semigroup
  • Г -semigroup
  • prime ideal
  • hull-kernel topology

MSC 2010

  • 20M12
  • 20Mxx
Accès libre

Order of Finite Soft Quasigroups with Application to Egalitarianism

Publié en ligne: 05 Apr 2022
Pages: 135 - 157

Résumé

Abstract

In this work, a soft set (F, A) was introduced over a quasigroup (Q,) and the study of finite soft quasigroup was carried out, motivated by the study of algebraic structures of soft sets. By introducing the order of a finite soft quasigroup, various inequality relationships that exist between the order of a finite quasigroup, the order of its soft quasigroup and the cardinality of its set of parameters were established. By introducing the arithmetic mean 𝒜ℱ(F, A) and geometric mean 𝒢ℱ(F, A) of a finite soft quasigroup (F, A), a sort of Lagrange’s Formula |(F, A)| = |A|𝒜ℱ(F, A) for finite soft quasigroup was gotten. Some of the inequalities gotten gave an upper bound for the order of a finite soft quasigroup in terms of the order of its quasigroup and cardinality of its set of parameters, and a lower bound for the order of the quasigroup in terms of the arithmetic mean of the finite soft quasigroup. A chain of inequalities called the Maclaurin’s inequality for any finite soft quasigroup (F, A)(Q,·) was shown to exist. A necessary and sufficient condition for a type of finite soft quasigroup to be extensible to a finite super soft quasigroup was established. This result is of practical use whenever a larger set of parameters is required. The results therein were illustrated with examples. Application to uniformity, equality and equity in distribution for social living is considered.

Mots clés

  • soft sets
  • quasigroups
  • soft quasigroups
  • soft subquasigroups
  • arithmetic and geometric mean
  • inequalities

MSC 2010

  • Primary 20N05, 03E72
  • Secondary 03E75
Accès libre

Disjunctive Ideals of Almost Distributive Lattices

Publié en ligne: 05 Apr 2022
Pages: 159 - 178

Résumé

Abstract

The concept of disjunctive ideals is introduced in an Almost Distributive Lattice (ADL). It is proved that the set of all disjunctive ideals of an ADL forms a complete lattice. A necessary and sufficient condition is derived for an inverse homomorphic image of a disjunctive ideal of an ADL to be again a disjunctive ideal. Later, the concept of strongly disjunctive ideals is introduced in an ADL and their properties are studied. Some equivalent conditions are established for the set of all strongly disjunctive ideals to convert into a sublattice of the ideal lattice.

Mots clés

  • Almost Distributive Lattice (ADL)
  • normal ADL
  • disjunctive ideal
  • strongly disjunctive ideal
  • normal prime ideal
  • minimal prime ideal

MSC 2010

  • 06D99
  • 06D15
Accès libre

Fuzzy Distributive Pairs in Fuzzy Lattices

Publié en ligne: 05 Apr 2022
Pages: 179 - 199

Résumé

Abstract

We generalize the concept of a fuzzy distributive lattice by introducing the concepts of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair in a fuzzy lattice. A relationship among a fuzzy join-distributive pair, a fuzzy join-semidistributive pair and a fuzzy join-modular pair is proved. It is shown that for a pair of fuzzy atoms, the notions of a fuzzy join-distributive pair and a fuzzy join-semidistributive pair coincide.

Mots clés

  • fuzzy lattices
  • fuzzy modular pair
  • fuzzy distributive pair
  • fuzzy semi-distributive pair

MSC 2010

  • 03B52
  • 03E72
  • 06D72
  • 06D99
Accès libre

Study of Additively Regular Г -Semirings and Derivations

Publié en ligne: 05 Apr 2022
Pages: 201 - 215

Résumé

Abstract

In this paper, the notions of commutator and derivation in additively regular -semirings with (A2, Г)-condition are introduced. We also characterize Jordan product for additively regular Г -semiring and establish some results which investigate the relationship between commutators, derivations and inner derivations. In 1957, E.C. Posner has shown that if there exists a non-zero centralizing derivation in a prime ring R, then R is commutative. This result is extended in the frame work of derivations of prime additively regular Г -semirings.

Mots clés

  • semirings
  • Г -semirings
  • additively regular Г -semirings
  • derivations and commutators

MSC 2010

  • 16Y60
  • 16Y99
Accès libre

Interior GE-Filters of GE-Algebras

Publié en ligne: 05 Apr 2022
Pages: 217 - 235

Résumé

Abstract

The notions of an interior GE-filter, a weak interior GE-filter and a belligerent interior GE-filter are introduced, and their relations and properties are investigated. Example of a GE-filter which is neither an interior GE-filter nor a weak interior GE-filter is provided. Relations between a weak interior GE-filter and an interior GE-filter are discussed, and conditions under which every weak interior GE-filter is an interior GE-filter are investigated. Relations between a belligerent interior GE-filter and an interior GE-filter are displayed, and conditions for an interior GE-filter to be a belligerent interior GE-filter are considered. Given a subset and an element, an interior GE-filter is established, and conditions for a subset to be a belligerent interior GE-filter are discussed. The extensibility of the beligerant interior GE-filter is debated. Relationships between weak interior GE-filter and belligerent interior GE-filter of type 1, type 2 and type 3 are founded.

Mots clés

  • (transitive, left exchangeable) GE-algebra
  • GE-filter
  • belligerent GE-filter
  • (weak) interior GE-filter
  • belligerent interior GE-filter (of type 1, type 2 and type 3)

MSC 2010

  • 03G25
  • 06F35

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