A ring R is called periodic if, for every a in R, there exist two distinct positive integers m and n
such that am= an. The paper is devoted to a comprehensive study of the periodicity of …

UJ-rings are studied, ie ring in which all units can be presented in a form 1+ x, for some x\in
J (R). The behavior of UJ-rings under various algebraic construction is investigated. In …

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 …

For a skew PBW extension over a right duo compatible ring, we characterize several kinds of
their elements such as units, idempotent, von Neumann regular, $\pi $-regular and the clean …

For a fixed natural number m≥ 2, an element a of a ring R is m-nil clean if a= e+ b where
em= e∈ R and b is nilpotent; if further eb= be, a is called strongly m-nil clean. The ring R is …

Question 3 of [3] asks whether the matrix ring M n (R) is nil clean, for any nil clean ring R. It is
shown that, positive answer to this question is equivalent to positive solution for Köthe's …

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 …

ABSTRACT UJ-rings are studied, ie, ring in which all units can be presented in a form 1+ x,
for some x∈ J (R). The behavior of UJ-rings under various algebraic construction is …

Let R be an associative unital ring with an endomorphism α and α-derivation δ. Some types
of ring elements such as the units and the idempotents play distinguished roles in …

The aim of this paper is to study idempotents and units in certain matrix rings over
polynomial rings. More precisely, the conditions under which an element in M_2(Z_px) for …