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2003 | 23 | 2 | 115-123
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Representable dually residuated lattice-ordered monoids

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EN
Abstrakty
EN
Dually residuated lattice-ordered monoids (DRl-monoids) generalize lattice-ordered groups and include also some algebras related to fuzzy logic (e.g. GMV-algebras and pseudo BL-algebras). In the paper, we give some necessary and sufficient conditions for a DRl-monoid to be representable (i.e. a subdirect product of totally ordered DRl-monoids) and we prove that the class of representable DRl-monoids is a variety.
Twórcy
autor
  • Department of Algebra and Geometry, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
Bibliografia
  • [1] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, New York 1981.
  • [2] A. Di Nola, G. Georgescu, and A. Iorgulescu, Pseudo BL-algebras: Part I, Mult.-Valued Logic 8 (2002), 673-714.
  • [3] A. Di Nola, G. Georgescu, and A. Iorgulescu, Pseudo BL-algebras: Part II, Mult.-Valued Logic 8 (2002), 717-750.
  • [4] A. Dvurecenskij, On pseudo MV-algebras, Soft Comput. 5 (2001), 347-354.
  • [5] A. Dvurecenskij, States on pseudo MV-algebras, Studia Logica 68 (2001), 301-327.
  • [6] G. Georgescu, and A. Iorgulescu, Pseudo MV- algebras, Mult.-Valued Logic 6 (2001), 95-135.
  • [7] A.M.W. Glass, Partially Ordered Groups, World Scientific, Singapore-New Jersey-London-Hong Kong 1999.
  • [8] G. Grätzer, General Lattice Theory, Birkhäuser, Basel-Boston-Berlin 1998.
  • [9] M.E. Hansen, Minimal prime ideals in autometrized algebras, Czechoslovak Math. J. 44 (119) (1994), 81-90.
  • [10] T. Kovár, A general theory of dually residuated lattice-ordered monoids, Ph.D. thesis, Palacký University, Olomouc 1996.
  • [11] T. Kovár, Two remarks on dually residuated lattice-ordered semigroups, Math. Slovaca 49 (1999), 17-18.
  • [12] J. Kühr, Ideals of non-commutative DRl-monoids, Czechoslovak Math. J., to appear.
  • [13] J. Kühr, Pseudo BL-algebras and DRl-monoids, Math. Bohem. 128 (2003), 199-208.
  • [14] J. Kühr, Prime ideals and polars in DRl-monoids and pseudo BL-algebras, Math. Slovaca 53 (2003), 233-246.
  • [15] J. Rach unek, MV-algebras are categorically equivalent to a class of DRl1(i)-semigroups, Math. Bohem. 123 (1998), 437-441.
  • [16] J. Rach unek, A duality between algebras of basic logic and bounded representable DRl-monoids, Math. Bohem. 126 (2001), 561-569.
  • [17] J. Rach unek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (127) (2002), 255-273.
  • [18] K.L.N. Swamy, Dually residuated lattice-ordered semigroups. I, Math. Ann. 159 (1965), 105-114.
  • [19] K.L.N. Swamy, Dually residuated lattice-ordered semigroups. III, Math. Ann. 167 (1966), 71-74.
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1067
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