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

Chen, Huanyin

• Published : 2012.05.31
• 55 13

#### 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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#### Cited by

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2. Nil-quasipolar rings vol.20, pp.1, 2014, https://doi.org/10.1007/s40590-014-0005-y
3. Strongly Clean Matrices Over Power Series vol.56, pp.2, 2016, https://doi.org/10.5666/KMJ.2016.56.2.387