Subdirectly irreducible members of products of lattice varieties-Reference-Cited by-同舟云学术

Subdirectly irreducible members of products of lattice varieties

Published:1988 Issue:3 Volume:102 Page:483-489
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Grätzer George,Kelly David

Abstract

In this paper we prove: Theorem. Let V \mathbf {V} and W \mathbf {W} be nontrivial lattice varieties. If L ∈ V ∘ W L \in \mathbf {V} \circ \mathbf {W} , then there is a subdirectly irreducible S ∈ V ∘ W S \in \mathbf {V} \circ \mathbf {W} containing L L as a sublattice. Moreover, if L L is finite, S S can also be chosen to be finite.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1988-102-03/S0002-9939-1988-0928965-4/S0002-9939-1988-0928965-4.pdf

Reference10 articles.

1. Interval lattices and the amalgamation property;Berman, Joel;Algebra Universalis,1981

2. Idempotents in the groupoid of all 𝑆𝑃 classes of lattices;Day, Alan;Canad. Math. Bull.,1978

3. G. Grätzer, General lattice theory, Pure and Appl. Math. Series, Academic Press, New York; Mathematische Reihe, Band 52, Birkhäuser Verlag, Basel; Akademie Verlag, Berlin, 1978. (Russian translation: "MIR", Moscow, 1982.)

4. On a special type of subdirectly irreducible lattice with an application to products of varieties;Grätzer, George;C. R. Math. Rep. Acad. Sci. Canada,1980

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