This is a continuation of [3]. We deal with algebras of type : T ! N. Assume that V is a variety of type . Let p = x be a strongly nonregular identity satised in V , i.e. x; y are variables of p and x =6 y . For a variety K 2 L; E; R; S or RS denotes the set of all, regular, symmetric or regular and symmetric identities satised in K, respectively.

This is an abstract of the paper to be submitted to Houston Journal of Mathematics. Our nomenclature and notation will be basically those of [3]. We shall consider algebras of type : T ! N, where T is a nonempty set, and N the set of all positive integers. By V we denote the set of all variables occurring in a polynomial symbol p. An identity p = q is called strongly non-regular if it is of the form p = (...) x for some binary polynomial symbol p, such that x; y 2 V and x =6 y. Let R denote the set of all regular identities of type . If K is a class of algebras of type , then E denotes the set of all identities satised by all algebras in K. We put R = E \ R. A variety K is called strongly non-regular if E contains some strongly non-regular identity. If is a set of identities of type , then K denotes the variety of algebras of type generated by ; E() will be the set of all identities which are consequences of . We put R() = E() \ R. We write ` e if there exists a nite proof of e starting from. (shrink)