A ring R is strongly 2-nil-clean if every element in R is the sum of two idempotents and a
nilpotent that commute. Fundamental properties of such rings are obtained. We prove that a …

Rings in which elements are sums of nilpotents, idempotents and tripotents Page 1 Journal of
Algebra and Its Applications Vol. 17, No. 1 (2018) 1850009 (7 pages) c© World Scientific …

A ring R is called periodic if, for every a in R, there exist two distinct positive integers m and n
such that am= an. The paper is devoted to a comprehensive study of the periodicity of …

When is every matrix over a ring the sum of two tripotents? - ScienceDirect Skip to main
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Abstract Motivated by Hirano-Tominaga's work on rings for which every element is a sum of
two idempotents and by de Seguins Pazzis's results on decomposing every matrix over a …

STRONGLY q-NIL-CLEAN RINGS Page 1 Siberian Mathematical Journal, vol. 60, no. 2, pp.
197–208, 2019 Russian Text c 2019 Abyzov AN STRONGLY q-NIL-CLEAN RINGS AN Abyzov …

We introduce a new class of generalized inverse which is called π− Hirano inverse. In this
paper some elementary properties of the π− Hirano inverse are obtained. We prove that a∈ …

For n≥ 2 and for a ring R, the notation P n (R) means that rn− r is nilpotent for all r∈ R. In
this paper, rings R for which P n (R) holds are completely characterized for any integers n≥ …

arXiv:1704.01303v1 [math.RA] 5 Apr 2017 Page 1 arXiv:1704.01303v1 [math.RA] 5 Apr 2017
WEAKLY TRIPOTENT RINGS S. BREAZ, A. CÎMPEAN Abstract. We study the class of rings R …

Let R be a ring and n be a positive integer. In this paper, further results on the n-strong
Drazin inverse are obtained in a ring. We prove that a∈ R is n-strongly Drazin invertible if …