Minimal varieties and quasivarieties-Reference-Cited by-同舟云学术

Minimal varieties and quasivarieties

Published:1990-02 Issue:1 Volume:48 Page:133-147
ISSN:0263-6115
Container-title:Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
language:en
Short-container-title:J Aust Math Soc A

Author:

Bergman Clifford,McKenzie Ralph

Abstract

AbstractWe prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the sett of unary term perations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics,Statistics and Probability

Reference9 articles.

1. Every idempotent plain algebra generates a minimal variety

2. On varieties of cylindric algebras with applications to logic

3. Idempotent algebras with restrictions on subalgebras;Szendrei;Acta Sci. Math.,1987

Cited by 22 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Structural and universal completeness in algebra and logic;Annals of Pure and Applied Logic;2024-03

2. Quasivarieties of Wajsberg hoops;Fuzzy Sets and Systems;2023-08

3. Universal Algebraic Methods for Non-classical Logics;Outstanding Contributions to Logic;2021-12-14

4. Every minimal dual discriminator variety is minimal as a quasivariety;Algebra universalis;2021-04-29

5. Singly generated quasivarieties and residuated structures;Mathematical Logic Quarterly;2020-06-21