Answer to a 1971 Question of Grätzer and Lakser on Pseudocomplemented Lattices-Reference-Cited by-同舟云学术

Answer to a 1971 Question of Grätzer and Lakser on Pseudocomplemented Lattices

Published:2024-06-17 Issue:1 Volume:30_NS4 Page:1-13
ISSN:0865-2090
Container-title:Mathematica Pannonica
language:
Short-container-title:MathPann

Author:

Farley Jonathan David¹

Affiliation:

1. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

Abstract

Grätzer and Lakser asked in the 1971 Transactions of the American Mathematical Society if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by 𝟐𝑛 ⊕ 𝟏 can be characterized by the property of not having a *-homomorphism onto 𝟐𝑖 ⊕ 𝟏 for 1 < 𝑖 < 𝑛.In this article, their question from 1971 is answered.

Publisher

Akademiai Kiado Zrt.

Link

https://akjournals.com/downloadpdf/journals/314/30_NS4/1/article-p1.xml

Reference22 articles.

1. [1]Balbes, R., and Dwinger, P. Distributive Lattices. University of Missouri Press, Columbia, Missouri, 1974.

2. [2]Bergman, C. Amalgamation classes of some distributive varieties. Algebra Universalis 20 (1985), 143-166.

3. [3]Bergman, C., McKenzie, R., and Nagy, Zs. How to cancel a linearly ordered exponent. Colloquia Mathematica Societatis János Bolyai 29. Universal Algebra, Esztergom (Hungary), 1977. (North-Holland, Amsterdam-New York, 1982), 87-93.

4. [4]Cornish, W. H. Ordered topological spaces and the coproduct of bounded distributive lattices. Colloquium Mathematicum 36 (1976), 27-35.

5. [5]Davey, B. A., and Priestley, H. A. Partition-induced natural dualities for varieties of pseudo-complemented distributive lattices. Discrete Mathematics 113 (1993), 41-58.