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arXiv · 2102.10460

Decompositions of Matrices into Potent and Square-Zero Matrices

Peter Danchev·Esther Garcia·Miguel Gomez Lozano
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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).

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Peter Danchev, Esther Garcia, Miguel Gomez Lozano. 2021-02-20. Decompositions of Matrices into Potent and Square-Zero Matrices. https://arxiv.org/abs/2102.10460

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