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Commutative directoids with sectionally antitone bijections

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EN
Abstrakty
EN
We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
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
  • Institute of Mathematics University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary
Bibliografia
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  • [2] I. Chajda, Lattices and semilattices having an antitone bijection in any upper interval, Comment. Math. Univ. Carolinae 44 (2003), 577-585.
  • [3] I. Chajda, G. Eigenthaler and H. Länger, Congruence Classes in Universal Algebra, Heldermann Verlag, Lemgo (Germany), 2003, ISBN 3-88538-226-1.
  • [4] I. Chajda and M. Kolařík, Directoids with sectionally antitone involutions and skew MV-algebras, Math. Bohemica 132 (2007), 407-422.
  • [5] I. Chajda and R. Radeleczki, Semilattices with sectionally antitone bijections, Novi Sad J. Math. 35 (2005), 93-101.
  • [6] B. Csákány, Characterization of regular varieties, Acta Sci. Math. Szeged 31 (1970), 187-189.
  • [7] J. Hagemann and A. Mitschke, On n-permutable congruences, Algebra Universalis 3 (1973), 8-12.
  • [8] J. Ježek and R. Quackenbush, Directoids: algebraic models of up-directed sets, Algebra Universalis 27 (1990), 49-69.
  • [9] V.M. Kopytov and Z.I. Dimitrov, On directed groups, Siberian Math. J. 30 (1989), 895-902. (Russian original: Sibirsk. Mat. Zh. 30 (6) (1988), 78-86.)
  • [10] S. Radeleczki, The congruence lattice of implication algebras, Math. Pannonica 3 (1992), 115-123.
  • [11] V. Snášel, λ-lattices, Math. Bohemica 122 (1997), 267-272.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1136
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