In this paper we obtain some equivalent conditions for strongly equiprime Γ− near rings N and the strongly equiprime radical Pse (N) coincides with Pse (L) where Pse (L) is the strongly equiprime radical of left operator near-ring L of N.

We give a new constructive definition for Noetherian rings. It has a very concrete statement and is nevertheless strong enough to prove constructively the termination of algorithms involving “trees of ideals”. The efficiency of such algorithms (at least for providing clear and intuitive constructive proofs) is illustrated in a section about Lasker–Noether rings: we give constructive proofs for ...

Let R be an associative ring with identity, C(R) denote the center of R, and g(x) be a polynomial in the polynomial ring C(R)[x]. R is called strongly g(x)-clean if every element r ∈ R can be written as r = s+u with g(s) = 0, u a unit of R, and su = us. The relation between strongly g(x)-clean rings and strongly clean rings is determined, some general properties of strongly g(x)-clean rings are...

Abstract Regarding the question of how idempotent elements affect reversible property rings, we study a version reversibility depending on idempotents. In this perspective, introduce right (resp., left )

martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.