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

Yıl 2018, Cilt: 5 Sayı: 3, 117 - 127, 08.10.2018

Kota Nagalakshmi Rajeswari Umesh Gupta

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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