Representation by triples of algebras with an MV-retract

Abstract

We introduce the notion of generalized rotation of a residuated lattice and characterize the varieties of bounded residuated lattices they generate, which we name MVR n . These algebras have a retraction onto a hyperarchimedean MV-algebra. Then we characterize algebras in MVR n as triples made of an MV-algebra, a residuated lattice with a nucleus, and an operator joining them.