A note on commutative weakly nil clean rings

Stancu, Alin

doi:10.1142/s0219498816200012

Cited by 16 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the fourth one, we examine the tensor products of algebras in the context of the periodicity as our basic results are, respectively, structured in Theorems 4.2 and 4.4. Thus, our results supply those from [60].…”

Section: Introductionsupporting

confidence: 86%

See 1 more Smart Citation

Rings close to periodic with applications to matrix, endomorphism and group rings

Abyzov¹,

Barati²,

Danchev³

2023

Preprint

View full text Add to dashboard Cite

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 R being nil-clean implies that M n (R) is nil-clean for all n ≥ 1 is paralleling to the corresponding implication for (Abelian, local) periodic rings. Besides, we study when the endomorphism ring E(G) of an Abelian group G is periodic. Concretely, we establish that E(G) is periodic exactly when G is finite as well as we find a complete necessary and sufficient condition when the endomorphism ring over an Abelian group is strongly m-nil clean for some natural number m thus refining an "old" result concerning strongly nil-clean endomorphism rings. Responding to a question when a group ring is periodic, we show that if R is a right (resp., left) perfect periodic ring and G is a locally finite group, then the group ring RG is periodic, too. We finally find some criteria under certain conditions when the tensor product of two periodic algebras over a commutative ring is again periodic. In addition, some other sorts of rings very close to periodic rings, namely the so-called weakly periodic rings, are also investigated.

show abstract

Section: Introductionsupporting

confidence: 86%

“…It is worthwhile noticing that some valuable results on tensor products of (weakly) nil-clean rings were obtained in [60].…”

Section: Tensor Product Of Algebrasmentioning

confidence: 99%

Rings close to periodic with applications to matrix, endomorphism and group rings

Abyzov¹,

Barati²,

Danchev³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…As a consequence of Lemma 2.3, every center of a Yaqub nil-clean ring is Yaqub nil-clean. This generalizes [12,Theorem 2] as well.…”

Section: Elementary Characterizationssupporting

confidence: 77%

On Yaqub nil-clean ring

Chen,

Abdolyousefi

2017

Preprint

View full text Add to dashboard Cite

show abstract

“…A ring R is weakly nil-clean provided that every element in R is the sum or difference of a nilpotent and an idempotent [1]. The subjects of nil-clean rings and weakly nil-clean rings are interested for so many mathematicians, e.g., [1,2,3,5,6,9,10,12] and [13].…”

Section: Introductionmentioning

confidence: 99%

Rings over which every matrix is the sum of a tripotent and a nilpotent

Sheibani,

Chen

2017

Preprint

View full text Add to dashboard Cite

A ring R is trinil clean if every element in R is the sum of a tripotent and a nilpotent. If R is a 2-primal strongly 2-nil-clean ring, we prove that M n (R) is trinil clean for all n ∈ N. Furthermore, we show that the matrix ring over a strongly 2-nil-clean ring of bounded index is trinil clean. We thereby provide various type of rings over which every matrix is the sum of a tripotent and a nilpotent.

show abstract

A note on commutative weakly nil clean rings

Cited by 16 publications

References 5 publications

Rings close to periodic with applications to matrix, endomorphism and group rings

Rings close to periodic with applications to matrix, endomorphism and group rings

On Yaqub nil-clean ring

Rings over which every matrix is the sum of a tripotent and a nilpotent

Contact Info

Product

Resources

About