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 …

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 …

This paper concerns the formal matrix ring Mn (R; s) over a ring R defined by a central
element s in R. Various basic properties of these rings are established; the isomorphism …

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

We examine those matrix rings whose entries lie in periodic rings equipped with some
additional properties. Specifically, we prove that the famous Diesl's question whether or not …

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 …

Abstract Let Λ _ (0, 0)=\left (A\;\;\;\;\;\;\; _A N_B _B M_A\;\;\;\; B\cr\right) Λ (0 0)=(AANBBMAB)
be a Morita ring, where the bimodule homomorphisms ϕ and ψ are zero. We study the finite …

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 …

Characterizations of Morita context rings satisfying various additional ring properties,
including reflexive, semiprime, prime, NI, weakly 2-primal and 2-primal, are given. The …

Recall that an n-by-n generalized matrix ring is defined in terms of sets of rings-bimodules
and bimodule homomorphisms, where the set of diagonal matrix units form a complete set of …