Matrices play an important role in both pure and applied mathematics. Matrices with entries
in rings have been intensively studied and used (eg, see [22, 87]); as well as matrices with …

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 …

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 …

Большое значение матриц для математики и её приложений общеизвестно. Прежде
всего это относится к числовым матрицам. Активно изучаются и используются также …

An element of a ring is called strongly nil clean provided that it can be written as the sum of
an idempotent and a nilpotent element that commute. We characterize, in this article, the …

In this paper, we introduce the notions of m-clean and strongly m-clean ring as
generalizations of clean ring and strongly clean ring respectively. We prove that if a ring R is …

A ring R is quasipolar if for any a∈ R, there exists p 2= p∈ R such that p∈ comm2 (a), p+
a∈ U (R) and ap∈ R qnil. In this article, we determine when a 2× 2 matrix over a …

Nicholson proved in [16] that in the study of some important properties of rings it is important
to know when we can decompose some (or all) elements of a ring as a sum of an …

The article concerns the question of when a generalized matrix ring K s (R) over a local ring
R is quasipolar. For a commutative local ring R, it is proved that K s (R) is quasipolar if and …

A ring R is called pseudopolar if for every a∈ R there exists p2= p∈ R such that p∈ comm 2
(a), a+ p∈ U (R) and akp∈ J (R) for some positive integer k. Pseudopolar rings are closely …