Power algebras and generalized quotient algebras

Abstract

The notion of a good quotient relation has been introduced as an attempt to generalize the notion of a quotient algebra to relations on an algebra which are not necessarily congruences. In order to make it possible to prove generalized versions of "power isomorphism theorems", the more restrictive notions of very good, Hoare good and Smyth good relation have been introduced. In this paper we describe the relationships between Hoare good, Smyth good and very good relations. As a consequence, we prove that every structure preserving relation on an algebra is very good.