Some varieties of algebraic systems of type ((n),(m))

摘要

In the present paper, we classify varieties of algebraic systems of the type ((n), (m)), for natural numbers n and m, which are closed under particular derived algebraic systems. If we replace in an algebraic system the n-ary operation by an n-ary term operation and the m-ary relation by the m-ary relation generated by an m-ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.