Subreducts of MV-algebras with product and product residuation

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 ŁΠ-algebras. In this paper we treat subreducts of ŁΠ-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 ŁΠ-algebras. In some cases, connections are given by means of equivalences of categories.

Authors and Affiliations

1. Department of Mathematics, University of Siena, Via del Capitano 15, 53100, Siena, Italy

   Franco Montagna

Corresponding author

Correspondence to Franco Montagna.

Dedicated to the Memory of Wim Blok

Received June 19, 2002; accepted in final form November 29, 2004.

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