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 …

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 …

A commutative ring R has Property (A) if every finitely generated ideal of R consisting
entirely of zero-divisors has a nonzero annihilator. We continue in this paper the study of …

Let R be an associative ring with identity, S a multiplicative subset of R, and M a right R-
module. Then M is called an S-Noetherian module if for each submodule N of M, there exist …

We examine those matrix rings whose entries lie in periodic rings equipped with some
additional properties. Specifically, we prove that the famous Diesl's question whether or not …

Let R be a ring with a monomorphism α and an α-derivation δ. We introduce (α, δ)-weakly
rigid rings which are a generalisation of α-rigid rings and investigate their properties. Every …

Based on a theorem of McCoy on commutative rings, Nielsen called a ring R right McCoy if,
for any nonzero polynomials f (x), g (x) over R, f (x) g (x)= 0 implies f (x) r= 0 for some 0≠ r∊ …

In, Nielsen proves that all reversible rings are McCoy and gives an example of a
semicommutative ring that is not right McCoy. At the same time, he also shows that …

We say that a*-ring R is a generalized quasi-Baer*-ring if for any ideal I of R, the right
annihilator of I n is generated, as a right ideal, by a projection, for some positive integer n …

A ring R is (strongly) weakly nil clean if every element in R is the sum or difference of a
nilpotent and an idempotent (that commutes). In this note, we show that if R is strongly nil …