One Chain Generated Varieties of MV-Algebras

Lattice of subalgebras in the finitely generated varieties of MV-algebras

In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras. With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of suba...

Boolean algebras R-generated by MV-effect algebras

We prove that every MV-effect algebra M is, as an effect algebra, a homomorphic image of its R-generated Boolean algebra. We characterize central elements of M in terms of the constructed homomorphism. 1. Definitions and basic relationships An effect algebra is a partial algebra (E;⊕, 0, 1) with a binary partial operation ⊕ and two nullary operations 0, 1 satisfying the following conditions. (E...

FREE ALGEBRAS IN VARIETIES OF BL-ALGEBRAS GENERATED BY A BLn-CHAIN

Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of Ln and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the...

Subvarieties of varieties generated by graph algebras

Bernoulli Automorphisms of Finitely Generated Free Mv-algebras

MV-algebras can be viewed either as the Lindenbaum algebras of Lukasiewicz infinite-valued logic, or as unit intervals [0, u] of lattice-ordered abelian groups in which a strong order unit u > 0 has been fixed. They form an equational class, and the free n-generated free MV-algebra is representable as an algebra of piecewise-linear continuous functions with integer coefficients over the unit n-...