TYPE-2 SUBDIRECTLY-IRREDUCIBLE ALGEBRAS IN FINITELY DECIDABLE VARIETIES

Let V be a finitely decidable variety and A is an element of V a finit e subdirectly irreducible algebra with a type 2 monolith mu. We prove that (1) the solvable radical nu of A is the centralizer of mu; (2) nu is abelian, i.e., every solvable congruence of A is abelian; (3) the interval sublattice I[nu, 1(A)] subset of or equal to Con A is linear, and typ{nu, a(A)} is an element of {3}. (C) 1995 Academic Press, Inc.