This paper is focused on the commutativity of laws semiprime rings, which satisfy some algebraic identities involving homoderivations ideals. It provides new and notable results that will interest researchers in this field, such as “R contains a nonzero central ideal if R admits homoderivation δ I δ(I)⊆Z where ring with center Z R”. Moreover, research also generalizes previously published liter...

in this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. we characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.

In this paper, we initiate the study of prime bi-ideals (fuzzy bi-ideals) in semirings. We define strongly prime, prime, semiprime, irreducible and strongly irreducible bi-ideals in semirings. We also define strongly prime, semiprime, irreducible, strongly irreducible fuzzy bi-ideals of semirings. We characterize those semirings in which each bi-ideal (fuzzy bi-ideal) is prime (strongly prime).

In this paper, properties of ideal I semiprime ring R with multiplicative generalized (α,β)- reverse derivation determined not necessarily additive map d is studied. We previous studies for different derivations to F. show that [β(p),d(p)]I=0 all p∈I or [d(p)],α(p)]I=0 under the given conditions. Also, we give relationship between and anti-automorphism α automorphism β R. Under conditions, exam...

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.

out, R will represent an associative ring with center Z(R). As usual the commutator xy−yx will be denoted by [x,y]. We will use basic commutator identities [xy,z] = [x,z]y+x[y,z] and [x,yz]= [x,y]z+y[x,z]. Recall that a ring R is prime if aRb = (0) implies that a = 0 or b = 0, and is semiprime if aRa = (0) implies a = 0. An additive mapping x x∗ on a ring R is called involution in case (xy)∗ = ...

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

In this paper, we introduce the notions of interval-valued fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each interval-valued fuzzy bi-ideal is semiprime and strongly prime.

The aim of this paper is to define a new kind of fuzzy gamma ring. So the concepts of fuzzy gamma ring, fuzzy ideal, fuzzy quotient gamma ring, and fuzzy gamma homomorphism are introduced.