Matrix rank 1 semigroup identities

摘要

A finite basis of identities is constructed for the semigroup of all rank 1 n #xD7; n matri#xAD;ces over the field. It is worthy to notice that every semigroup of all rank r, r l,n#xD7;n matrices over a finite field has no finite basis of identities. Let G be an arbitrary vari#xAD;ety of groups with a finite basis of identities. A finite basis of identities is constructed for the variety generated by all completely 0-simple semigroups over G-groups.