Journal ArticleDOI
Every idempotent plain algebra generates a minimal variety
About:
This article is published in Algebra Universalis.The article was published on 1988-12-01. It has received 13 citations till now. The article focuses on the topics: Variety (universal algebra) & Idempotence.read more
Citations
More filters
Journal ArticleDOI
The Relationship Between Two Commutators
Keith A. Kearnes,Ágnes Szendrei +1 more
TL;DR: It is derived that if A is an abelian algebra and (A) satisfies an idempotent Mal'cev condition which fails to hold in the variety of semilattices, then A is affine, and it is refined by showing that abelIAN algebras are quasi-affine in such varieties.
Posted Content
The relationship between two commutators
Keith A. Kearnes,Ágnes Szendrei +1 more
TL;DR: In this paper, it was shown that the linear commutator is definable in terms of the centralizer relation in any variety satisfying a nontrivial idempotent Mal'cev condition.
Journal ArticleDOI
Minimal varieties and quasivarieties
Clifford Bergman,Ralph McKenzie +1 more
TL;DR: In this paper, it was shown that every locally finite, congruence modular, minimal variety is minimal as a quasi-variety, such that the set of unary term operations forms a group.
Journal ArticleDOI
Almost all minimal idempotent varieties are congruence modular
TL;DR: In this article, it was shown that a minimal idempotent variety that is not congruence distributive is term equivalent to a variety of sets, the variety of semilattices, or a number of affine modules over a simple ring.
References
More filters
BookDOI
The two-valued iterative systems of mathematical logic
TL;DR: In this paper, the authors present an approach to coordinate and apply closed-systems in the field of computer vision and artificial intelligence applications, based on the concept of co-ordination.
Journal ArticleDOI
Commutator theory for congruence modular varieties
Ralph Freese,Ralph McKenzie +1 more
TL;DR: The theory of commutators in congruence modular varieties has been studied in this article, where it has been shown that a commutator can be defined naturally in the lattice of normal subgroups.
Book
Mal'cev Varieties
TL;DR: Rudiments and notations as mentioned in this paper : Centrality, direct decomposition, central isotopy and cancellation, plain algebras and equational completeness, extensions and obstructions.