On algebras of the variety B1,1

Аннотация

By B_1,1 we denote the variety of unary algebras of signature f, g which is defined by the identity fg(x) = x. In this note it is proved that B_1,1 is a cover for the variety A_1,1, where A_1,1 is the variety defined by the identities fg(x) = x = gf(x). It is also shown that each endomorphism of a strongly connected algebra from B_1,1 is an automorphism.