Search

The notion of rough sets was introduced by Z. Pawlak in 1982. The concept of G-semihyperring is a generalization of semihyperring, Γ-semiring and semiring. In this paper, we study the notion of a rough (rough prime) ideal in a Γ-semihyperring. Also, we discuss the relation between the upper and lower rough ideals and the upper and lower approximation of their homomorphism images. [ABSTRACT FROM AUTHOR]

Let R be a commutative Noetherian ring and I, J two ideals of R. Let M be a finitely generated R-module; it is shown that (1) if dimR/(I+J)=0, then HI,Ji (M)/JHI,Ji (M) is I-cofinite Artinian for all i ≥ 0; let dimRM/JM = d (2) if R is local and S is a non-zero Serre subcategory of the category of R-modules satisfying the condition CI , then HI,Jd (M)/JHI,Jd (M) ϵ S (3) if M has finite Krull dimension, then HI,Jd+1 (M)/JHI,Jd+1 (M) = 0. Furthermore, notion of (I,J)-relative Goldie dimension of modules is defined and it is shown that HI,Jn (M)/JHI,Jn (M) is Artinian, whenever M is a ZD-module of dimension n such that the (I,J)-relative Goldie dimension of any quotient of M is finite. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize thosesemigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. [ABSTRACT FROM AUTHOR]