Nil-clean matrix rings

By Simion Breaz, G. Călugăreanu, Peter Danchev, T. Micu. 2013

103 citations recorded by the source corpus.

We characterize the nil clean matrix rings over fields. As a by product, it is proved that the full matrix rings with coefficients in commutative nil-clean rings are nil-clean, and we obtain a complete characterization of the finite rank Abelian groups with nil clean endomorphism ring and the Abelian groups with strongly nil clean endomorphism ring, respectively.

Subfields: Algebra and Number Theory

View Paper: https://www.semanticscholar.org/paper/43b0e5dfc44769bfa25604db1014692bb14fc8a0

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In Algebra and Number Theory

1. Peter Danchev
2. Warren Wm. McGovern
3. Yiqiang Zhou
4. Simion Breaz
5. A. Diesl

Citations in the corpus

• Rings in which every element is either a sum or a difference of a nilpotent and an idempotent (2014, background): “The sufficiency follows directly from [2], so that let we now treat the necessity.”
• Commutative weakly nil clean unital rings (2015, background): “For a classification of when Mn(R) is nil clean the interested reader can see in [5] or [18].”