Decompositions of Matrices into Potent and Square-Zero Matrices
Rings and Algebras
2021-02-23 v1 Representation Theory
Abstract
In order to find a suitable expression of an arbitrary square matrix over an arbitrary finite commutative ring, we prove that every such a matrix is always representable as a sum of a potent matrix and a nilpotent matrix of order at most two when the Jacobson radical of the ring has zero-square. This somewhat extends results of ours in Lin. & Multilin. Algebra (2021) established for matrices considered on arbitrary fields. Our main theorem also improves on recent results due to Abyzov et al. in Mat. Zametki (2017), \v{S}ter in Lin. Algebra & Appl. (2018) and Shitov in Indag. Math. (2019).
Cite
@article{arxiv.2102.10460,
title = {Decompositions of Matrices into Potent and Square-Zero Matrices},
author = {Peter Danchev and Esther Garcia and Miguel Gomez Lozano},
journal= {arXiv preprint arXiv:2102.10460},
year = {2021}
}
Comments
10 pages