# SOME STRONGLY NIL CLEAN MATRICES OVER LOCAL RINGS

• Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
• Published : 2011.07.31

#### 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. A ring is strongly nil clean in case each of its elements is strongly nil clean. We investigate, in this article, the strongly nil cleanness of 2${\times}$2 matrices over local rings. For commutative local rings, we characterize strongly nil cleanness in terms of solvability of quadratic equations. The strongly nil cleanness of a single triangular matrix is studied as well.

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#### Cited by

1. Quasipolar Subrings of 3 x 3 Matrix Rings vol.21, pp.3, 2013, https://doi.org/10.2478/auom-2013-0048
2. Nil clean rings vol.383, 2013, https://doi.org/10.1016/j.jalgebra.2013.02.020
3. Nil-quasipolar rings vol.20, pp.1, 2014, https://doi.org/10.1007/s40590-014-0005-y