An element a of a ring R is nil-clean if a= e+ b where e 2= e∈ R and b is a nilpotent; if further
eb= be, the element a is called strongly nil-clean. The ring R is called nil-clean (resp …

An element of a ring is called strongly J-clean provided that it can be written as the sum of an
idempotent and an element in its Jacobson radical that commute. A ring is strongly J-clean …

A ring is called uniquely clean if every element is uniquely the sum of an idempotent and a
unit. The rings described by the title include uniquely clean rings, and they arise as …

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 …

The notion of quasipolar elements of rings was introduced by Koliha and Patricio in 2002. In
this paper, we introduce the notion of quasipolar rings and relate it to other familiar notions …

A*-ring R is called a*-clean ring if every element of R is the sum of a unit and a projection,
and R is called a strongly*-clean ring if every element of R is the sum of a unit and a …

We consider and study those rings in which each nil-clean or clean element is uniquely nil-
clean. We establish that, for abelian rings, these rings have a satisfactory description and …

An element of a ring R is called clean if it is the sum of an idempotent and a unit. A ring R is
called clean if each of its element is clean. An element r\in R called regular if r= ryr for some …

A ring R is uniquely (nil) clean in case for any a∈ R there exists a unique idempotent e∈ R
such that a− e∈ R is invertible (nilpotent). We prove in this article that a ring R is uniquely …

We consider in-depth and characterize in certain aspects those rings whose non-units are
strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In …