On the semigroup of square matrices

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 $M(n,\mathbb{F})$.

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

References in corpus (1)

• On conjugacy in regular epigroups