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2004 | 24 | 1 | 63-74
Tytuł artykułu

Direct decompositions of dually residuated lattice-ordered monoids

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EN
Abstrakty
EN
The class of dually residuated lattice ordered monoids (DRl-monoids) contains, in an appropriate signature, all l-groups, Brouwerian algebras, MV- and GMV-algebras, BL- and pseudo BL-algebras, etc. In the paper we study direct products and decompositions of DRl-monoids in general and we characterize ideals of DRl-monoids which are direct factors. The results are then applicable to all above mentioned special classes of DRl-monoids.
Twórcy
  • Department of Algebra and Geometry, Faculty of Sciences, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic
  • Department of Mathematical Methods in Economy, Faculty of Economics, VŠB-Technical University of Ostrava, Sokolská 33, 701 21 Ostrava, Czech Republic
Bibliografia
  • [1] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Foundations of Many-valued Reasoning, Kluwer Acad. Publ., Dordrecht 2000.
  • [2] A. Di Nola, G. Georgescu and A. Iorgulescu, Pseudo BL-algebras: Part I, Multiple-Valued Logic 8 (2002), 673-714.
  • [3] P. Hájek, Metamathematics of Fuzzy Logic, Kluwer Acad. Publ., Dordrecht 1998.
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  • [5] T. Kovár, A general theory of dually residuated lattice-ordered monoids, Ph.D. Thesis, Palacký Univ., Olomouc 1996.
  • [6] J. Kühr, Pseudo BL-algebras and DRl-monoids, Math. Bohemica 128 (2003), 199-208.
  • [7] J. Kühr, Prime ideals and polars in DRl-monoids and pseudo BL-algebras, Math. Slovaca 53 (2003), 233-246.
  • [8] J. Kühr, Ideals of noncommutative DRl-monoids, Czechoslovak Math. J. (to appear).
  • [9] J. Rachnek, Prime ideals in autometrized algebras, Czechoslovak Math. J. 37 (112) (1987), 65-69.
  • [10] J. Rachnek, Polars in autometrized algebras, Czechoslovak Math. J. 39 (114) (1989), 681-685.
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  • [12] J. Rachnek, DRl-semigroups and MV-algebras, Czechoslovak Math. J. 48 (123) (1998), 365-372.
  • [13] J. Rachnek, MV-algebras are categorically equivalent to a class of DRl-semigroups, Math. Bohemica 123 (1998), 437-441.
  • [14] J. Rachnek, A duality between algebras of basic logic and bounded representable DRl-monoids, Math. Bohemica 126 (2001), 561-569.
  • [15] J. Rachnek, Polars and annihilators in representable DRl- monoids and MV-algebras, Math. Slovaca 51 (2001), 1-12.
  • [16] J. Rachnek, A non-commutative generalization of MV-algebras, Czechoslovak Math. J. 52 (127) (2002), 255-273.
  • [17] J. Rachnek, Prime ideals and polars in generalized MV- algebras, Multiple-Valued Logic 8 (2002), 127-137.
  • [18] J. Rachnek, Prime spectra of non-commutative generalizations of MV-algebras, Algebra Univers. 48 (2002), 151-169.
  • [19] D. Salounová, Lex-ideals of DRl-monoids and GMV-algebras, Math. Slovaca 53 (2003), 321-330.
  • [20] K.L.N. Swamy, Dually residuated lattice-ordered semigroups I, Math. Ann. 159 (1965), 105-114.
  • [21] K.L.N. Swamy, Dually residuated lattice-ordered semigroups II, Math. Ann. 160 (1965), 64-71.
  • [22] K.L.N. Swamy, Dually residuated lattice-ordered semigroups III, Math. Ann. 167 (1966), 71-74.
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  • [24] K.L.N. Swamy, and B.V. Subba Rao, Isometries in dually residuated lattice-ordered semigroups, Math. Sem. Notes Kobe Univ. 8 (1980). doi: 369-379
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1076
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