arXiv subjects

Venus Amjid

Publications and source records attributed to Venus Amjid.

4 recordsLinked to original sources

arXiv2010

Ideals in intra-regular left almost semigroups

In this paper, we have introduced the notion of (1,2)-ideal in an LA-semigroup and shown that (1,2)-ideal and two-sided ideal coincide in an intra-regular LA-semigroup. We have characterized an intra-regular LA-semigroup by using the properties of left and right ideals. Some natural examples of LA-semigroups have been given. Further we have investigated some useful conditions for an LA-semigroup to become an intra-regular LA-semigroup and given the counter examples to illustrate the converse inclusions. All the ideals (left, right, two-sided, interior, quasi, bi- generalized bi- and (1,2)) of an intra-regular LA-semigroup have been characterized. Finally we have given an equivalent statement for a two-sided ideal of an intra-regular LA-semigroup in terms of the intersection of two minimal two-sided ideals of an intra-regular LA-semigroup.

math.GR↗

arXiv2010

Γ-Abel-Grassmann's groupoids characterized by their intuitionistic Γ-ideals

In this paper, we have discussed several properties of intuitionistic fuzzy Γ-ideals of a Γ-AG-groupoid which is the generalization of ideals in AG-groupoid We have characterized an intra-regular Γ-AG^{**}-groupoid in terms of intuitionistic fuzzy Γ-left (right, two-sided) ideals, intuitionistic fuzzy (Γ-generalized bi) Γ-bi-ideals, intuitionistic fuzzy Γ-interior ideals and intuitionistic fuzzy Γ-quasi ideals. We have proved that the intuitionistic fuzzy Γ-left (right, interior, quasi) ideals coincide in an intra-regular Γ-AG^{**}-groupoid. We have also shown that the set of intuitionistic fuzzy Γ-two-sided ideals of an intra-regular Γ-AG^{**}-groupoid forms a semilattice structure.

math.GR↗

arXiv2010

Characterizations of intra-regular gamma AG-groupoids by the properties of their gamma ideals

We have characterized an intra-regular Γ-AG^{**}-groupoids by using the properties of Γ-ideals (left, right, two-sided ), Γ-interior, Γ-quasi, Γ-bi and Γ-generalized bi and Γ-(1,2)). We have prove that all the Γ-ideals coincides in an intra-regular Γ-AG^{**}-groupoids. It has been examined that all the Γ-ideals of an intra-regular Γ-AG^{**}-groupoids are Γ-idempotent. In this paper we define all Γ-ideals in Γ-AG^{**}-groupoids and we generalize some results.

math.GR↗

arXiv2010

On some classes of Abel-Grassmann's groupoids

In this paper, we have investigated different classes of an AG-groupoid by their structural properties. We have prove that weakly regular, intra-regular, right regular, left regular, left quasi regular and completely regular coincide in an AG-groupoid with left identity and in AG^{**}-groupoid. Further we have prove that every regular (weakly regular, intra-regular, right regular, left regular, left quasi regular, completely regular) AG-groupoid with left identity (AG^{**}-groupoid) is regular but the converse is not true in general. Also it has been shown that non-associative regular, weakly regular, intra-regular, right regular, left regular, left quasi regular and completely regular AG^{*} groupoids do not exist.

math.GR↗