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Two remarks on Lie rings of 2 × 2 matrices over commutative associative rings

Evgenii L. Bashkirov (2020)

Commentationes Mathematicae Universitatis Carolinae

Let C be an associative commutative ring with 1. If a C , then a C denotes the principal ideal generated by a . Let l , m , n be nonzero elements of C such that m n l C . The set of matrices a 11 a 12 a 21 - a 11 , where a 11 l C , a 12 m C , a 21 n C , forms a Lie ring under Lie multiplication and matrix addition. The paper studies properties of these Lie rings.

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