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http://dx.doi.org/10.4134/BKMS.2012.49.3.589

STRONGLY NIL CLEAN MATRICES OVER R[x]/(x2-1)  

Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.3, 2012 , pp. 589-599 More about this Journal
Abstract
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 $R[x]/(x^2-1)$ 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;
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