Equational theories of algebras with distributive congruences-Reference-Cited by-同舟云学术

Equational theories of algebras with distributive congruences

Published:1973 Issue:2 Volume:41 Page:373-377
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Padmanabhan R.,Quackenbush R. W.

Abstract

If an equational class of algebras has the distributive or permutable congruence property then it is well known that it satisfies certain conditions, known as Mal’cev-type conditions. In this note such Mal’cev-type conditions are used to find minimal bases for certain equational theories of algebras. A typical result states that every finitely based equational theory of algebras with distributive and permutable congruences is one-based.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1973-041-02/S0002-9939-1973-0325498-2/S0002-9939-1973-0325498-2.pdf

Reference8 articles.

1. Primitive satisfaction and equational problems for lattices and other algebras;Baker, Kirby A.;Trans. Amer. Math. Soc.,1974

2. Algebras whose congruence lattices are distributive;Jónsson, Bjarni;Math. Scand.,1967

3. G. Gratzer and R. McKenzie, Equational spectra and reduction of identities, Notices Amer. Math. Soc. 14 (1967), 697. Abstract #67T-469.

4. Thomas C. Green, Minimum bases for equational theories of groups and rings (preprint).

5. Equational bases for lattice theories;McKenzie, Ralph;Math. Scand.,1970

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