• Corpus ID: 59324588

Direct product factors in GMV-algebras

  title={Direct product factors in GMV-algebras},
  author={Jir{\'i} Rachunek and Dana Salounov{\'a}},
  journal={Mathematica Slovaca},
GMV-algebras are non-commutative generalizations of MV-alge­ bras and by A. Dvurecenskij they can be represented as intervals of unital lattice ordered groups. Moreover, they are polynomially equivalent to dually residuated ^-monoids (DP£-monoids) from a certain variety of DH^-monoids. In the paper, using these correspondences, direct product factors in GMV-algebras are introduced and studied and the lattices of direct factors are described. Further, the polars of projectable GMV-algebras are… 
Direct summands and retract mappings of generalized MV-algebras
In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained
On isometries in GMV-algebras
Let A = (A,⊕,−,∼, 0, 1) be a GMV-algebra and ρ: A × A → A the distance function on A defined by ρ(x, y) = (x∨y)−(x∧y) for each x, y ∈ A.In this note it is shown that a mapping f: A → A such that ρ(a,


Direct decompositions of dually residuated lattice-ordered monoids
The class of dually residuated lattice ordered monoids (DR`-monoids) contains, in an appropriate signature, all `-groups, Brouwerian algebras, MV and GMV -algebras, BLand pseudo BL-algebras, etc. In
Prime spectra of non-commutative generalizations of MV-algebras
Abstract. Non-commutative generalizations of MV-algebras were introduced by G. Georgescu and A. Iorgulesco as well as by the author; the generalizations are equivalent and are called GMV-algebras. We
Ideals of noncommutative DRℓ-monoids
In this paper, we introduce the concept of an ideal of a noncommutative dually residuated lattice ordered monoid and we show that congruence relations and certain ideals are in a one-to-one
Algebraic analysis of many valued logics
This paper is an attempt at developing a theory of algebraic systems that would correspond in a natural fashion to the No-valued propositional calculus(2). For want of a better name, we shall call
A non-commutative generalization of MV-algebras
Groupes et anneaux réticulés
Direct product decompositions of pseudo $MV$-algebras
Partially Ordered Groups, World Scientific, Singapore-New Jersey- London-Hong
  • 1999