Preserving of ideals on generalized induced algebras

Abstract

Substituting for the fundamental operations of an algebra term operations, we get a new algebra of the same type, called a generalized derived algebra. Such substitutions are called generalized hypersubstitutions. Generalized hypersubstitutions can also be applied to every equation of a fully invariant equational theory. The equational theory generated by the resulting set of the equations induces on every algebra of the type under consideration a fully invariant congruence relation. If we factorize the generalized derived algebra by this fully invariant congruence relation, then we will obtain an algebra which we call a generalized induced algebra. In this paper, we use a generalization of the concept of an ideal to a universal algebra and ask for the properties of in the algebra Aσ induced by the generalized hypersubstitution σ. © 2011 Pushpa Publishing House.