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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 …

We study the rings over which each square matrix is the sum of an idempotent matrix and a
q-potent matrix. We also show that if F is a finite field not isomorphic to 𝔽_3 and q>1 is odd …

In this article, we define a graded trinil clean ring graded by a group. The behavior of the
property of being trinil clean is studied in ring constructions of graded group rings, graded …

Исследованы кольца, каждая квадратная матрица над которыми представима в виде
суммы идемпотентной матрицы и q-потентной матрицы. Показано, что если F …

This article presents the concept of a NE-nil clean ring, which is a generalization of the
strongly nil clean ring. A ring R is considered NE-nil clean if, for every a in R, there exists a1 …

An element is known a strongly nil* clean element if, where, are idempotents and is
nilpotent, that commute with one another. An ideal of a ring is called a strongly nil* clean …

An element is known a strongly nil* clean element if a= e 1-e 1 e 2+ n, where e 1, e 2 are
idempotents and n is nilpotent, that commute with one another. An ideal I of a ring R is called …