• Corpus ID: 59324588

Direct product factors in GMV-algebras

@article{Rachunek2005DirectPF,
  title={Direct product factors in GMV-algebras},
  author={Jir{\'i} Rachunek and Dana Salounov{\'a}},
  journal={Mathematica Slovaca},
  year={2005},
  volume={55},
  pages={399-407}
}
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,

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  • 1999