MATRIX RANK-1 SEMIGROUP IDENTITIES

A finite basis of identities is constructed for the semigroup of all r ank 1 n x n matrices over the field. It is worthy to notice that every semigroup of all rank r, r > 1, n x n matrices over a finite field ha s no finite basis of identities. Let G be an arbitrary variety of grou ps with a finite basis of identities. A finite basis of identities is constructed for the variety generated by all completely 0-simple semig roups over G-groups.