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On the semigroup of square matrices

Ganna Kudryavtseva·Volodymyr Mazorchuk
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Abstract

We study the structure of nilpotent subsemigroups in the semigroup $M(n,\mathbb{F})$ of all $n\times n$ matrices over a field, $\mathbb{F}$, with respect to the operation of the usual matrix multiplication. We describe the maximal subsemigroups among the nilpotent subsemigroups of a fixed nilpotency degree and classify them up to isomorphism. We also describe isolated and completely isolated subsemigroups and conjugated elements in $M(n,\mathbb{F})$.

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Ganna Kudryavtseva, Volodymyr Mazorchuk. 2005-10-28. On the semigroup of square matrices. https://arxiv.org/abs/math/0510624

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