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The Gorbunov-Tumanov conjecture on the structure of lattices of quasivarieties is proved true for the case of algebraic lattices.
Namely, for an algebraic atomistic lattice L, the following conditions are equivalent: (1) L is represented as Lq(K) for some algebraic quasivariety K; (2) L is represented as SΛ (A) for some algebraic lattice A which satisfies the minimality condition and nearly satisfies the maximality conditions;
(3) L is a coalgebraic lattice admitting an equaclosure operator.
Supported by RFFR grants Nos. 96-01-01525 and 96-0-000976, and by DFG grant No. 436 (RUS) 113/2670.
Translated from Algebra i Logika, Vol. 36, No. 4, pp. 363–386, July–August, 1997. 相似文献
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C. Jayaram 《Algebra Universalis》2006,55(2-3):297-303
In this paper we establish several equivalent conditions for an algebraic lattice to be a finite Boolean algebra.
This paper is dedicated to Walter Taylor.
Received February 11, 2005; accepted in final form October 9, 2005. 相似文献
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Antonio Ferná ndez Ló pez Eulalia Garcí a Rus 《Proceedings of the American Mathematical Society》1998,126(11):3211-3221
Uniform elements in algebraic lattices are studied and their relationship with some nonassociative extensions of Goldie's Second Theorem is shown.
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Claus Scheiderer 《Algebra Universalis》1986,22(2-3):235-243
It is shown that the lattice of all closed subgroups of a compact topological group and the lattice of all connected closed subgroups of a pro-Lie group are algebraic, even arithmetic, if they are equipped with the order opposite to the natural one. The compact elements form ideals in these lattices and are explicitly determined. In the course of the proof the question is treated whether forming lattices of closed subgroups of topological groups commutes with projective limits.Presented by Laszlo Fuchs. 相似文献
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In this paper, we give a short proof of the following result of G. Grätzer and E. T. Schmidt: every m-algebraic lattice can be represented as the lattice of m-complete congruence relations of some m-complete modular lattice.Dedicated to Bjarni Jonsson on his 70th birthdayThe research of the first author was supported by the NSERC of Canada.The research of the third author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903. 相似文献
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Hans-E. Porst 《Algebra Universalis》2011,65(3):285-298
We show that subobjects and quotients respectively of any object K in a locally finitely presentable category form an algebraic lattice. The same holds for the internal equivalence relations on K. In fact, these results turn out to be??at least in the case of subobjects??nothing but simple consequences of well known closure properties of the classes of locally finitely presentable categories and accessible categories, respectively. We thus get a completely categorical explanation of the well known fact that the subobject- and congruence lattices of algebras in finitary varieties are algebraic. Moreover we also obtain new natural examples: in particular, for any (not necessarily finitary) polynomial set-functor F, the subcoalgebras of an F-coalgebra form an algebraic lattice; the same holds for the lattices of regular congruences and quotients of these F-coalgebras. 相似文献
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Josef Niederle 《Mathematica Slovaca》2008,58(1):1-4
Relationship between automorphisms and residuated bounded mappings in atomistic lattices is studied.
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