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

#### Chercher

#### Résumé

In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid

#### Mots clés

- hyperring
- semiprime hyperring
- generalized centroid
- regular hyperring

#### MSC 2010

- 20N20
- 16Y20

#### Résumé

In this paper, we introduce the notion of a (strong) hyper

#### Mots clés

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

#### MSC 2010

- 03B50
- 06D35
- 03E72

#### Résumé

In this paper, the notions of

#### Mots clés

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

#### MSC 2010

- 03G25
- 06F35

#### Résumé

In this paper, we transfer Davey‘s characterization for

#### Mots clés

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

#### MSC 2010

- Primary: 06B10
- Secondary: 06D22, 08A30, 08B10

#### Résumé

The notion of prime ideals is introduced in transitive

#### 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

Pages: 121 - 134

#### Résumé

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

Pages: 135 - 157

#### Résumé

In this work, a soft set (_{(}_{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

Pages: 159 - 178

#### Résumé

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

#### Résumé

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

Pages: 201 - 215

#### Résumé

In this paper, the notions of commutator and derivation in additively regular -semirings with (_{2}, 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

#### Mots clés

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

#### MSC 2010

- 16Y60
- 16Y99

#### Résumé

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