Relative MV-algebras and relative homomorphisms
Antonio Di Nola, Ada Lettieri · Mathematica Slovaca · 2009
Abstract In this paper we define the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of interval subalgebra of A; this has been already studied in the literature. Applying these notions, two new categories denoted as r and int are introduced. In both cases the objects are MV-algebras, but the homomorphisms are defined by means of relative subalgebras or by interval subalgebras, respectively. The relations occurring between these categories and the category of all MV-algebras with usual homomorphisms are investigated. The main results of the paper deal with one-generated free MV-algebras in the variety generated by the finite chains S i, i ⩽ p (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra.