On the semigroup of square matrices
Abstract
We study the structure of nilpotent subsemigroups in the semigroup
M(n,F)
of all
n×n
matrices over a field,
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,F)
.