In this paper, we introduce the notion of primal strong co-ideals and give some results involving them. It is shown thatsubtractive strong co-ideals are intersection of all primal strong co-ideals that contain them. Also we prove that the representation of strong co-ideals as reduced intersections of primal strong co-ideals is unique.

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...

in this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup s . some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. different classes, regular, intra-regular, and simple ordered semigroups are   characterized by means of fuzzy sof...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

The foldness of PI( , , ⊆)BCK -ideals and PI(⊆, ⊆, ⊆)BCK -ideals is considered, and their properties are investigated. Hyper homomorphic inverse image of PI( , , ⊆)BCK -ideals, PI( , ⊆, ⊆)BCK -ideals, PI(⊆, ⊆, ⊆)BCK -ideals, and PI( , , )BCK -ideals are discussed.

Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

In this paper we introduce the definitions of generalized ideals and generalized filters in pseudo effect algebras. From the generalized ideals (filters), we obtain some equivalent characterization of ideals (filters). The relationships among generalized ideals, ideals and local ideals are studied in detail. We also establish an isomorphism between the set of supports and the set of generalized...