On normal and regular identities (Q749564)

Let V be a variety; an identity \(p=q\) in V is called regular if the set of all variables occurring in p and q coincides, normal if p and q are the same variables or neither p nor q is a variable. The word problem for free algebras of the variety defined by all normal identities of V is solvable iff it is solvable for V, which is due to a property of regular identities proved by the author in Beitr. Algebra Geom. 24, 41-49 (1987; Zbl 0615.08003). Some properties for the lattice of subvarieties of the normal part of a variety V are given, and some results on the existence of finite bases for the regular and normal part of V are added.