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On varieties of MV-algebras with internal states.
No full textRecently A. Di Nola and A. Dvurecˇenskij introduced the variety SMV of MV-algebras with an internal operator,state MV-algebras. Successively they gave a stronger version of state MV-algebras, calledstate-morphism MV-algebras. In this paper we continue the studies presented above justlooking at several proper subvarieties of SMV, obtained by imposing suitable conditions on
the behavior of the internal operator
Relative MV-algebras and relative homomorphisms
No full textIn the paper is defined the notion of relative subalgebra of an MV-algebra A. A particular case of this notion is the notion of an interval subalgebra of A, which has been already studied in the literature. Applying these notions, two new categories denoted as rMV and intMV 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 MV-chains Si , 0<i< p +1 (p varying over the set of all positive integers) and their relations to certain relative subalgebras of the cyclic free MV-algebra
Determining the Schein rank of matrices over linear lattices and finite relational equations
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