On the Semigroup of Square Matrices.

We study the structure of nilpotent subsemigroups in the semigroup M(n,픽) of all n×n matrices over a field 픽 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,픽). [ABSTRACT FROM AUTHOR]