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1-Sylvester matrices
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DOI：10.1515/spma-2025-0044.png)
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Abstract
En 中文
A nonzero element a a is called 1-Sylvester in a ring R R , if there exist b , c is an element of R b,c\in R such that 1 = a b + c a 1=ab+ca . In this article, we study such elements, mainly in matrix rings over commutative rings. In particular, we study the case when b = c b=c , when b b is called an anticommutator inverse for a a .
Keywords:
Sylvester equation
idempotent
unit
nilpotent
matrix
1-Sylvester element
anticommutator inverse