Nil-clean matrix rings
Commutative Algebra
2013-10-02 v1 Rings and Algebras
Representation Theory
Abstract
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.
Cite
@article{arxiv.1310.0416,
title = {Nil-clean matrix rings},
author = {S. Breaz and G. Călugăreanu and P. Danchev and T. Micu},
journal= {arXiv preprint arXiv:1310.0416},
year = {2013}
}
Comments
Preprint version, accepted by "Linear Algebra and its Applications"