Bull. Korean Math. Soc. 2012; 49(3): 589-599
Printed May 1, 2012
https://doi.org/10.4134/BKMS.2012.49.3.589
Copyright © The Korean Mathematical Society.
Huanyin Chen
Hangzhou Normal University
An element of a ring is called strongly nil clean provided that it can be written as the sum of an idempotent and a nilpotent element that commute. We characterize, in this article, the strongly nil cleanness of $2\times 2$ and $3\times 3$ matrices over $R[x]/\big(x^2-1\big)$ where $R$ is a commutative local ring with characteristic $2$. Matrix decompositions over fields are derived as special cases.
Keywords: strongly nil matrix, characteristic polynomial, local ring
MSC numbers: 15A23, 13H99, 13B25
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