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On Unit Nil-Clean Rings

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0 Published in 2019 at "Mediterranean Journal of Mathematics"

DOI: 10.1007/s00009-019-1369-z

Abstract: A ring R is unit nil-clean if, for any $$a\in R$$a∈R, there exists a unit $$u\in R$$u∈R, such that ua is the sum of an idempotent and a nilpotent. In this paper, we completely describe… read more here.

Keywords: clean rings; unit nil; unit; nil clean ... See more keywords

Rings additively generated by idempotents and nilpotents

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0 Published in 2020 at "Communications in Algebra"

DOI: 10.1080/00927872.2020.1852410

Abstract: Abstract A ring R is a strongly 2-nil-clean if every element in R is the sum of two idempotents and a nilpotent that commute. A ring R is feebly clean if every element in R… read more here.

Keywords: rings additively; strongly nil; clean rings; generated idempotents ... See more keywords

Ideally nil clean rings

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1 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1929276

Abstract: Abstract A ring is called nil clean if every element can be written as the sum of an idempotent and a nilpotent. The class of nil clean rings has emerged as an important variant of… read more here.

Keywords: ideal; class; clean rings; ideally nil ... See more keywords

Nil-clean quadratic elements

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0 Published in 2017 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498817501973

Abstract: We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification… read more here.

Keywords: quadratic elements; clean quadratic; nil clean;

Strongly weakly nil-clean rings

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1 Published in 2017 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498817502334

Abstract: A ring R is strongly weakly nil-clean if every element in R is the sum or difference of a nilpotent and an idempotent that commutes. We prove, in this paper, that a ring R is… read more here.

Keywords: strongly weakly; clean rings; weakly nil; nil clean ... See more keywords

Rings additively generated by tripotents and nilpotents

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0 Published in 2019 at "Journal of Algebra and Its Applications"

DOI: 10.1142/s0219498819500506

Abstract: A ring [Formula: see text] is Zhou nil-clean if every element in [Formula: see text] is the sum of two tripotents and a nilpotent that commute. A ring [Formula: see text] is feebly clean if… read more here.

Keywords: nil clean; formula see; zhou nil; see text ... See more keywords

A Generalization of Strongly Nil Clean Rings

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1 Published in 2018 at "Algebra Colloquium"

DOI: 10.1142/s100538671800041x

Abstract: Generalizing the notion of strongly nil clean rings, we introduce strongly quasi-nil clean rings. Some fundamental properties and equivalent characterizations of this class of rings are provided. By means of g-Drazin inverses, Cline’s formula and… read more here.

Keywords: clean rings; strongly nil; generalization strongly; nil clean ... See more keywords