## Evgenii L. BashkirovTwo remarks on Lie rings of $2\times 2$ matrices over commutative associative rings

Comment.Math.Univ.Carolin. 61,1 (2020) 1-10.

Abstract:Let $C$ be an associative commutative ring with 1. If $a\in C$, then $aC$ denotes the principal ideal generated by $a$. Let $l, m, n$ be nonzero elements of $C$ such that $mn \in lC$. The set of matrices $\left( \begin{smallmatrix} a_{11} & a_{12} a_{21} & -a_{11} \end{smallmatrix} \right)$, where $a_{11}\in lC$, $a_{12}\in mC$, $a_{21}\in nC$, forms a Lie ring under Lie multiplication and matrix addition. The paper studies properties of these Lie rings.

Keywords: Lie ring; associative commutative ring; matrix

DOI: DOI 10.14712/1213-7243.2020.010
AMS Subject Classification: 17B05

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