Geodesic
Two remarks on Lie rings of $2\times 2$ matrices over commutative associative rings
Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 1-10.

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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.
DOI : 10.14712/1213-7243.2020.010
Classification : 17B05
Keywords: Lie ring; associative commutative ring; matrix 
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Bashkirov, Evgenii L. Two remarks on Lie rings of $2\times 2$ matrices over commutative associative rings. Commentationes Mathematicae Universitatis Carolinae, Tome 61 (2020) no. 1, pp. 1-10. doi : 10.14712/1213-7243.2020.010. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2020.010/

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