If N is a submodule of the R-module M , and a ∈ R, let λa : M/N → M/N be multiplication by a. We say that N is a primary submodule of M if N is proper and for every a, λa is either injective or nilpotent. Injectivity means that for all x ∈ M , we have ax ∈ N ⇒ x ∈ N . Nilpotence means that for some positive integer n, aM ⊆ N , that is, a belongs to the annihilator of M/N , denoted by ann(M/N). ...

By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

Abstract. The interval-valued prime fuzzy ideals (in brevity, the iv. prime fuzzy ideals) of a semigroup have been recently studied by Kar, Sarkar and Shum [18]. As a continued study of i-v fuzzy ideals, we are going to investigate the properties of i-v fuzzy quasi-ideal and i-v fuzzy bi-ideal of a semiring and then we characterize the regularity and intra-regularity of a semiring in terms of t...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

Let $R$ be a commutative ring with identity and $M$ be a unitary$R$-module. The primary-like spectrum $Spec_L(M)$ is thecollection of all primary-like submodules $Q$ such that $M/Q$ is aprimeful $R$-module. Here, $M$ is defined to be RSP if $rad(Q)$ isa prime submodule for all $Qin Spec_L(M)$. This class containsthe family of multiplication modules properly. The purpose of thispaper is to intro...

The objective of writing this manuscript is to apply the concept fuzzy set on some basic Hopf algebraic structures. In manuscript, novel concepts subalgebra, ideal, and H-submodule are proposed. Some properties these discussed, significant results also proved in it. advantages proposed work studied application discussed

The concepts of (∈γ ,∈γ ∨ qδ)-fuzzy h-ideals and (∈γ ,∈γ ∨ qδ)-fuzzy hinterior ideals in hemirings are introduced. Some new characterization theorems of these kinds of fuzzy h-ideals are also given. In particular, we investigate prime and strong prime (∈γ ,∈γ ∨ qδ)-fuzzy h-ideals in hemirings. Finally, we show that the h-hemiregular and h-semisimple hemirings can be described by using these kin...

The purpose of this paper is to study some properties of cartesian product of fuzzy completely prime ideals and fuzzy completely semiprime ideals of Γ-semigroups. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between cartesian product of fuzzy ideals (fuzzy completely prime ideals, fuzzy completely semiprime ideals) of a Γ-semigroup and that of it...

The main purpose of this paper is to continue the study of uniform strong primeness on fuzzy setting. A pure fuzzy notion of this structure allows us to develop specific fuzzy results on USP (uniformly strongly prime) ideals over commutative and noncommutative rings. Besides, the differences between crisp and fuzzy setting are investigated. For instance, in crisp setting an ideal I of a ring R ...

in this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. after obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. the number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. by exploiting the order, we label the s...