NDLI: Joins of subalgebras and normals in 0-regular varieties

Content Provider	Springer Nature Link
Author	McConnell, Nicholas Stokes, Tim
Copyright Year	2015
Abstract	In any 0-normal variety (0-regular variety in which {0} is a subalgebra), every congruence class containing 0 is a subalgebra. These “normal subalgebras” of a fixed algebra constitute a lattice, isomorphic to its congruence lattice. We are interested in those 0-normal varieties for which the join of two normal subalgebras in the lattice of normal subalgebras of an algebra equals their join in the lattice of subalgebras, as happens with groups and rings. We characterise this property in terms of a Mal’cev condition, and use examples to show it is strictly stronger than being ideal determined but strictly weaker than being 0-coherent (classically ideal determined) and does not imply congruence permutability.
Ending Page	304
Page Count	12
Starting Page	293
File Format	PDF
ISSN	00025240
e-ISSN	14208911
Journal	algebra universalis
Issue Number	3
Volume Number	74
Language	English
Publisher	Springer Basel
Publisher Date	2015-08-12
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	0-regular variety Mal’cev condition Algebra EQ-monoid ideal determined variety Equational classes, universal algebra
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

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Joins of subalgebras and normals in 0-regular varieties