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Porings and poring algebras

Autorzy Jun, Y.  Kim, H.  Neggers, J.
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN In this paper we define an algebra of type (2,2,0) associated with posets called a poring and we study several properties of porings and the linear algebras having such porings as their bases. In particular, we show that if (P; *, .) is a standard poring then the distributive law (x . y) * z = (x * z) . (y * z) holds iff the poset P (or the poset X) is (C2 +1)-free.
Słowa kluczowe
 PL algebra BCH   grupoidy   ślad EN BCH algebra   groupoids   trace   poring
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2006
Tom Vol. 39, nr 2
Strony 267--276
Opis fizyczny Bibliogr. 10 poz.
Twórcy
 autor Jun, Y. autor Kim, H. autor Neggers, J. Department of Mathematics Education Gyeongsang National University Chinju, 660-701, Korea, ybjun@gsnu.ac.kr
Bibliografia
[1] G. Grätzer, General Lattice Theory, Academic Press, New York, 1978.
[2] Kelly and I. Rival, Planar lattices, Canad. J. Math. 27 (1975), 636-665.
[3] Y. B. Jun, J. R. Kim and H. S. Kim. BCK-algebras inherited from the posets, Math. Japon. 45 (1997), 119-123.
[4] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul, 1994.
[5] J. Neggers, Partially ordered sets and groupoids, Kyungpook Math. J. 16 (1976), 7-20.
[6] J. Neggers and H. S. Kim, Modular semigroups and posets, Semigroup Forum 53 (1996), 57-62.
[7] J. Neggers and H. S. Kim, Self-distributive modular pogroupoids and posets, Kyungpook Math. J. 38 (1998), 407-409.
[8] J. Neggers and H. S. Kim, Basic Posets, World Scientific Publishing Co., New Jersey, 1998.
[9] J. Neggers and H. S. Kim, Algebras associated with posets, Demonstratio Math. 34 (2001), 13-23.
[10] J. Neggers, Y. H. Kim and H. S. Kim, Incomparability and transitivity, Kyungpook Math. J. 42(1) (2002), 5-11.
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