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 …

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 …

1. Introduction Page 1 International Journal of Mathematics, Game Theory and Algebra Volume
23, Number 2, pp. 1–14 ISSN 1060-9881 c 2014 Nova Science Publishers, Inc …

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 …

[2] Êî÷ åòîâà ÞÂ Декартова сумма решеточно K-упорÿдоченных алгебр//× ебышевский
сборник. 2012. Т. 13, Вып. 1. С. 92-101.[3] Êî÷ åòîâà ÞÂ, Øèðøîâà ÅÅ Первичный радикал …

КОЛЬЦА ФОРМАЛЬНЫХ МАТРИЦ И ИХ ИЗОМОРФИЗМЫ АНАбызов, ДТТапкин Page 1
Сибирский математический журнал Ноябрь декабрь, 2015. Том 56, № 6 УДК 512.55 …

An element in a ring is clean (or, unit-regular) if it is the sum (or, the product) of an
idempotent and a unit, and is nil-clean if it is the sum of an idempotent and a nilpotent …

In the present paper, we study formal matrix rings over a given ring and determinants of such
matrices. In Secs. 1–4, some general properties of formal matrix rings are presented. In …