An element a in a ring R is called almost clean if a can be written as a= r+ e, where r is a
regular (non zero-divisor) element and e is an idempotent. It is well known that C (X) is clean …

In this article we introduce the concept of strongly r-clean ring. The ring R is said to be
strongly r-clean ring if every element of R is sum of a regular element and an idempotent …

Let R be an associative ring with identity. Ring R is considered clean if each element is the
sum of an idempotent element and a unit element. A clean ring is generalized to an r-clean …

This article aims to introduce the concept of $ p-\mathrm {clean\ring}\mathrm {s} $ as a
generalization of some concepts such as $\mathrm {clean\rings} $ and $ r-\mathrm …

Let be a ring. Ring is said to be a clean ring if every element of R can be expressed as the
sum of a unit and an idempotent element. Furthermore, there are r-clean rings. An r-clean …

An element of a ring R is said to be r-precious if it can be written as the sum of a von
Neumann regular element, an idempotent element and a nilpotent element. If all the …

In this paper we introduce rings that satisfy regular 1-stable range. These rings are left-right
symmetric and are generalizations of unit 1-stable range. We investigate characterizations of …

In this paper, we study the transfer of some algebraic properties from the ring $ R $ to the
ring of skew Hurwitz series $(HR,\omega) $, where $\omega $ is an automorphism of $ R …

The concept of a clean ring, introduced by Nicholson in 1977, is defined as follows: for any
x∈ R, there exist e∈ Id (R) and u∈ U (R) such that x= e+ u. In this paper, the concept of a …

In 1977, Nicholson initially proposed the idea of a" clean ring," where the ring R is called a
clean ring if for each x∈ R there exist e∈ Id (R) and u∈ U (R) such that x= e+ u. This paper …