Many variations of the notions of clean and strongly clean have been studied by a variety of
authors. We develop a general theory, based on idempotents and direct sum …

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 …

We will completely characterize the commutative local rings for which Mn (R) is strongly
clean, in terms of factorization in R [t]. We also obtain similar elementwise results which …

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 …

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 strongly clean if every element of R is the sum of a unit and an idempotent
that commute with each other. A recent result of Borooah, Diesl and Dorsey [G. Borooah, AJ …

Let Ks (R) be the generalized matrix ring over a ring R with multiplier s. For a general local
ring R and a central element s in the Jacobson radical of R, necessary and sufficient …

We define the class of {\it CUSC} rings, that are those rings whose clean elements are
uniquely strongly clean. These rings are a common generalization of the so-called {\it USC} …

Nielsen proved that all reversible rings are McCoy and gave an example of a
semicommutative ring that is not right McCoy. When R is a reversible ring with an (α, δ) …

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent
and a unit that commute, and R is called strongly clean if every element of R is strongly …