Subreducts of MV-algebras with product and product residuation

摘要

Recently, MV-algebras with product have been investigated from different points of view. In particular, in [EGM01], a variety resulting from the combination of MV-algebras and product algebras (see [H98]) has been introduced. The elements of this variety are called LΠ-algebras. In this paper we treat subreducts of LΠ-algebras, with emphasis on quasivarieties of subreducts whose basic operations are continuous in the order topology. We give axiomatizations of the most interesting classes of subreducts, and we connect them with other algebraic classes of algebras, like f-rings and Wajsberg hoops, as well as to structures of co-infinitesimals of LΠ-algebras. In some cases, connections are given by means of equivalences of categories.