PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2009 | 29 | 1 | 5-19
Tytuł artykułu

Remarks on pseudo MV-algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Pseudo MV-algebras (see e.g., [4, 6, 8]) are non-commutative extension of MV-algebras. We show that every pseudo MV-algebra is isomorphic to the algebra of action functions where the binary operation is function composition, zero is x ∧ y and unit is x. Then we define the so-called difference functions in pseudo MV-algebras and show how a pseudo MV-algebra can be reconstructed by them.
Twórcy
autor
  • Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
  • Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic
Bibliografia
  • [1] S.L. Bloom, Z. Ésik and E. Manes, A Cayley theorem for Boolean algebras, Amer. Math. Monthly 97 (1990), 831-833.
  • [2] I. Chajda, A representation of the algebra of quasiordered logic by binary functions, Demonstratio Mathem. 27 (1994), 601-607.
  • [4] I. Chajda and H. Länger, Action algebras, Italian J. of Pure Appl. Mathem., submitted.
  • [5] I. Chajda and J. Kühr, Pseudo MV-algebras and meet-semilattices with sectionally antitone permutations, Math. Slovaca 56 (2006), 275-288.
  • [6] A. Dvurečenskij, Pseudo MV-algebras are intervals in l-groups, J. Aust. Math. Soc. 72 (3) (2002), 427-445.
  • [7] N. Galatos, P. Jipsen, T. Kowalski and H. Ono, Residuated Lattices, An Algebraic Glimpse at Substructural Logics, Elsevier 2007.
  • [8] G. Georgescu and A. Iorgelescu, Pseudo MV-algebras, Multiple Valued Log. 6 (2001), 95-135.
  • [9] A.M.W Glass and W.C. Holland, Lattice-Ordered Groups, Kluwer Acad. Publ., Dordrecht-Boston-London 1989.
  • [10] P. Jipsen and C. Tsinakis, A survey of Residuated Lattices, Ordered Agebraic Structures (Martinez J., editor), Kluwer Academic Publishers, Dordrecht, 2002, 19-56.
  • [11] J. Kühr and F. Švrček, Operators on unital l-groups, preprint, 2007.
  • [12] J. Rachůnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (2002), 255-273.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1148
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.