On the lattice of tolerances for a finite chain

• Autorzy: Górnicka A. , Grygiel J. , Tyrala I.

Identyfikatory

DOI

10.16926/m.2016.21.03

• Języki publikacji: EN

Abstrakty

EN

We provide some description of the lattice of tolerances for a finite chain, pointing to the skeleton tolerance as a special element of this lattice. In particular, we prove that the lattice of all glued tolerances of an n-element chain is isomorphic to the lattice of all tolerances of an n- 1-element chain nad at the same time is a principal filter of the lattice of an n-element chain.

Słowa kluczowe

EN

lattice of tolerance; algebraic grid; congruences

PL

krata tolerancji; siatka algebraiczna; kongruencja

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2016
• Tom: Vol. 21
• Strony: 25--30
• Opis fizyczny: Bibliogr. 11 poz.,. rys.

Twórcy

autor

Górnicka A.

• Jan Długosz University in Częstochowa, Institute of Mathematics and Computer Science, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland

autor

Grygiel J.

• Jan Długosz University in Częstochowa, Institute of Philosophy, al. Armii Krajowej 36a, 42-200 Częstochowa, Poland

autor

Tyrala I.

• Jan Długosz University in Czestochowa, Institute of Mathematics and Computer Science, al. Armii Krajowej 13/15, 42-200 Częstochowa, Poland

Bibliografia

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• [3] Ivan Chajda, Josef Dalík, Josef Niederle, Vítezslav Veselý, and Bohdan Zelinka. How to draw tolerance lattices of finite chains. Arch. Math. (Brno), 16:161–165, 1980.
• [4] Gábor Czédli. Factor lattices by tolerances. Acta Sci. Math. (Szeged), 44:35–42, 1982. 30
• [5] Gábor Czédli and George Grätzer. Lattice tolerances and congruences. Algebra Universalis, 66:5–6, 2011.
• [6] Gabor Czédli, Joanna Grygiel, and Katarzyna Grygiel. Distributive lattices determined by weighted double skeletons. Algebra Universalis, 69(4):313–326, 2013.
• [7] Gábor Czédli and Lajos Klukovits. A note on tolerances of idempotent algebras. Glasnik Matematicki (Zagreb), 18:35–38, 1983.
• [8] Bernhard Ganter and Rudolf Wille. Formal concept analysis. Mathematical Foundations. Springer-Verlag, 1999.
• [9] Anetta Górnicka, Joanna Grygiel, and Iwona Tyrala. Sparingly glued tolerances. Scientific Issues Jan Długosz University. Mathematics, XX:47–54, 2015.
• [10] Joanna Grygiel and Sándor Radeleczki. On the tolerance lattice of tolerance factors. Acta Mathematica Hungarica, 141(3):220–237, 2013.
• [11] Klaus Reuter. Counting formulas for glued lattices. Order, 1:265–276, 1985.