On the semigroup of square matrices

Details On the semigroup of square matrices On the semigroup of square matrices

2005-10-28

arxiv.org/abs/math/0510624v2

Algebra Colloq. 15 (2008), no. 1, 33-52

Mathematics

Group Theory

A revised version of the preprint: A. Kudryavtseva, V. Mazorchuk, Square matrices as a semigroup, Preprint 2002:18, Uppsala Un

Scientific paper

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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