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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2019. Vol. 29

A Note on Commutative Nil-Clean Corners in Unital Rings

Author(s)
P. V. Danchev
Abstract

We shall prove that if R is a ring with a family of orthogonal idempotents {ei}ni=1 having sum 1 such that each corner subring eiRei is commutative nil-clean, then R is too nil-clean, by showing that this assertion is actually equivalent to the statement established by Breaz-Călugăreanu-Danchev-Micu in Lin. Algebra & Appl. (2013) that if R is a commutative nil-clean ring, then the full matrix ring Mn(R) is also nil-clean for any size n. Likewise, the present proof somewhat supplies our recent result in Bull. Iran. Math. Soc. (2018) concerning strongly nil-clean corner rings as well as it gives a new strategy for further developments of the investigated theme.

About the Authors

Peter V. Danchev, Ph.D. (Math.), Prof., Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev st., bl. 8, Sofia, 1113, Bulgaria, e-mail: danchev@math.bas.bg; pvdanchev@yahoo.com

For citation

Danchev P.V. A Note on Commutative Nil-Clean Corners in Unital Rings. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 29, pp. 3-9. https://doi.org/10.26516/1997-7670.2019.29.3

This article has been updated.
An Addendum to this article was published on March 2020.

Keywords
nil-clean rings, nilpotents, idempotents, corners
UDC
512.552.13
MSC
16U99; 16E50; 13B99
DOI
https://doi.org/10.26516/1997-7670.2019.29.3
References
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