On Strongly Nil Clean Matrices

Chen, Huanyin

doi:10.1080/00927872.2011.637265

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Introduction4

-Primal S S H H H H H H H H H H H H H H H H H Nil-semicommut1

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Cited by 20 publications

(15 citation statements)

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“…These rings are extensively studied by many authors, namely, [1], [3], [4], [5] and [15]. Nicholson proved that every clean ring is exchange.…”

Section: -Primal S S H H H H H H H H H H H H H H H H H Nil-semicommutmentioning

confidence: 99%

Semicommutativity of the rings relative to prime radical

Kose¹,

Üngör²

2015

Commentationes Mathematicae Universitatis Carolinae

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“…These rings are extensively studied by many authors, namely, [1], [3], [4], [5] and [15]. Nicholson proved that every clean ring is exchange.…”

Section: -Primal S S H H H H H H H H H H H H H H H H H Nil-semicommutmentioning

confidence: 99%

Semicommutativity of the rings relative to prime radical

Kose¹,

Üngör²

2015

Commentationes Mathematicae Universitatis Carolinae

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“…In [2], Breaz, Danchev and Zhou de…ned a ring R to be weakly nil clean if each element r 2 R can be written as r = b + e or r = b e for b 2 N (R) and e 2 Id(R). We refer the reader to [8,1,3,5,7,4,2] for a survey on nil clean and weakly nil clean rings.…”

Section: Introductionmentioning

confidence: 99%

(WEAKLY) n

HANDAM¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. Let R be an associative ring with identity. For a positive integer n > 2, an element a 2 R is called n potent if a n = a . We de…ne R to be (weakly) n nil clean if every element in R can be written as a sum (a sum or a di¤erence) of a nilpotent and an n potent element in R. This concept is actually a generalization of weakly nil clean rings introduced by Danchev and McGovern,[6]. In this paper, we completely determine all n; m 2 N such that the ring of integers modulo m, Zm is (weakly) n nil clean.

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“…In [4], Breaz, Danchev and Zhou defined a ring R to be weakly nil clean if each element r ∈ R can be written as r = n + e or r = n − e for n ∈ N (R) and e ∈ Id(R). We refer the reader to [3,7,8,10,19,4] for a survey on nil clean and weakly nil clean rings.…”

Section: Introductionmentioning

confidence: 99%