Commutative directoids with sectionally antitone bijections

• Autorzy: Ivan Chajda , Miroslav Kolařík , Sándor Radeleczki
• Języki publikacji: 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.

Słowa kluczowe

EN

directoid; section antitone bijection; implication algebra; double implication algebra

Kategorie tematyczne

• 03G25: Other algebras related to logic
• 06A12: Semilattices
• 03G10: Lattices and related structures

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 77-89

Daty

wydano

2008

otrzymano

2007-03-05

poprawiono

2007-03-27

Twórcy

autor

Ivan Chajda

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

autor

Miroslav Kolařík

• Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00 Olomouc, Czech Republic

autor

Sándor Radeleczki

• Institute of Mathematics University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary

Bibliografia

• [1] J.C. Abbott, Semi-Boolean algebras, Matem. Vestnik 4 (1967), 177-198.
• [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.

Identyfikatory

DOI

10.7151/dmgaa.1136