In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...

Let R be a ring with center Z and I a nonzero ideal of R. An additive mapping F : R → R is called a generalized derivation of R if there exists a derivation d : R → R such that F xy F x y xd y for all x, y ∈ R. In the present paper, we prove that if F x, y ± x, y for all x, y ∈ I or F x ◦ y ± x ◦ y for all x, y ∈ I, then the semiprime ring R must contains a nonzero central ideal, provided d I /...

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) ⊆ L(X) be a standard operator algebra. Suppose there exists a linear mappi...

Let $G$ be a group with identity $e$. Let $R$ be a $G$-graded commutative ring with a non-zero identity and $M$ be a graded $R$-module. In this article, we introduce the concept of graded almost semiprime submodules. Also, we investigate some basic properties of graded almost semiprime and graded weakly semiprime submodules and give some characterizations of them.

Abstract It is proven that finite idempotent left non-degenerate set-theoretic solutions $(X,r)$ of the Yang–Baxter equation on a set $X$ are determined by simple semigroup structure (in particular, union isomorphic copies group) and some maps $q$ $\varphi _{x}$ $X$, for $x\in X$. This turns out to be group precisely when associated monoid $M(X,r)$ cancellative all equal an automorphism this gr...

In this paper we have extended neutrosophic LA-semigroup, neutrosophic sub LAsemigroup, neutrosophic ideals, neutosophic prime ideals, neutrosophic semiprime ideals, neutrosophic strong irreducible ideals to soft neutrosophic LA-semigroup,soft neutosophic sub LA-semigroup,soft neutrosophic ideals,soft neutrosophic prime ideals,soft neutrosophic semiprime ideals and soft strong irreducible neutr...

In this paper we have studied   q   , -fuzzy semiprime ideals in semigroups. We have characterized completely regular semigroups by the properties of their   q   , -fuzzy quasi ideals. Moreover we have characterized semigroups that are semilattices of groups by   q   , -fuzzy quasi ideals.

In a recent paper we have extended the classical Herstein's theorem on Jordan derivations on prime rings to Jordan superderivations on prime associative superalgebras. In the present paper we extend this result to semiprime associative superalgebras.

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.