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http://dx.doi.org/10.4134/BKMS.2011.48.4.759

SOME STRONGLY NIL CLEAN MATRICES OVER LOCAL RINGS  

Chen, Huanyin (Department of Mathematics Hangzhou Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.4, 2011 , pp. 759-767 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. 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.
Keywords
$2{\times}2$ matrix; strongly nil cleanness; local ring;
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