Characterization of $2\times 2$ nil-clean matrices over integral domains

Authors

DOI:

https://doi.org/10.13069/jacodesmath.451229

Keywords:

Nil-clean matrix, Idempotent matrix, Nil-potent matrix, Diophantine equation

Abstract

Let $R$ be any ring with identity. An element $a \in R$ is called nil-clean, if $a=e+n$ where $e$ is an idempotent element and $n$ is a nil-potent element. In this paper we give necessary and sufficient conditions for a $2\times 2$ matrix over an integral domain $R$ to be nil-clean.

Received: 16 October 2016 Accepted: 25 April 2018

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Published

2018-09-15

How to Cite

Rajeswari, K. N., & Gupta, U. (2018). Characterization of $2\times 2$ nil-clean matrices over integral domains. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(3), 117–127. https://doi.org/10.13069/jacodesmath.451229

Issue

Vol. 5 Issue 3: September 2018

Section

Articles