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Various conditions on a noncommutative ring imply that it is 2-primal (ie, the ring's prime
radical coincides with the set of nilpotent elements of the ring). We will examine several such …

We investigate von Neumann regularity of rings whose simple singular right R-modules are
GP-injective. It is proved that a ring; R is strongly regular iff R is a weakly right duo ring …

Mason introduced the reflexive property for ideals, and then this concept was generalized by
Kim and Baik, defining idempotent reflexive right ideals and rings. In this article, we …

An endomorphism α of a ring R is called right reversible if whenever ab= 0 for a, b∈ R, then
bα (a)= 0. A ring R is called right α-reversible if there exists a right reversible endomorphism …

We introduce weakly semicommutative rings which are a generalization of semicommutative
rings, and give some examples which show that weakly semicommutative rings need not be …

A ring R is called Armendariz if whenever the product of any two polynomials in R [x] over R
is zero, then so is the product of any pair of coefficients from the two polynomials. Such rings …

In this paper, we study the notion of McCoy ring over the class of non-commutative rings of
polynomial type known as skew Poincaré–Birkhoff–Witt extensions. As a consequence, we …

In this paper, we obtain a partial solution to the following question of Köthe: For which rings
$ R $ is it true that every left (or both left and right) $ R $-module is a direct sum of cyclic …

Semicommutative and Armendariz rings are a generalization of reduced rings, and
therefore, nilpotent elements play an important role in this class of rings. There are many …