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Demonstratio Mathematica

Tytuł artykułu

Externalization of lattices

Autorzy Chajda, I.  Wismath, S. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN Let r be a type of algebras. An identity s = t of type r is said to be externally compatible, or simply external, if the terms s and t are either the same variable or both start with the same operation symbol fj of the type. A variety is called external if all of its identities are external. For any variety V , there is a least external variety E(V ) containing V , the variety determined by the set of all external identities of V . External identities and varieties have been studied by [4], [5] and [2], and a general characterization of the algebras in E(V ) has been given in [3]. In this paper we study the algebras of the variety E(V ) where V is the type (2, 2) variety L of lattices. Algebras in L may also be described as ordered sets, and we give an ordered set description of the algebras in E(L). We show that on any algebra in E(L) there is a natural quasiorder having an additional property called externality, and that any set with such a quasiorder can be given the structure of an algebra in E(L). We also characterize algebras in E(L) by an inflation construction.
Słowa kluczowe
PL kraty   eksternalizacja krat  
EN externally compatible identity   lattice   externalization of lattices  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2006
Tom Vol. 39, nr 4
Strony 731--736
Opis fizyczny Bibliogr. 5 poz.
autor Chajda, I.
autor Wismath, S.
  • Department Algebra and Geometry Palacky University Tomkova 40, 779 00 Olomouc, Czech Republic,
[1] I. Chajda, Normally presented varieties, Algebra Universalis 34 (1995), 327–335.
[2] W. Chromik, Externally compatible identities of algebras, Demonstratio Math. 23 (1990), no. 2, 345–355.
[3] I. Chajda, K. Denecke and S. L. Wismath, A characterization of P-compatible varieties, to appear in Algebra Colloquium.
[4] J. Płonka, On varieties of algebras defined by identities of special forms, Houston Mathem. J. 14 (1988), 253–263.
[5] J. Płonka, P-compatible identities and their applications to classical algebras, Math. Slovaca 40 (1990), no. 1, 21–30.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-article-PWA5-0018-0001