Projective algebras and primitive subquasivarieties in varieties with factor congruences

We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its homomorphic image. Using this criterion of projectivity, we d...

Full description

Saved in:
Bibliographic Details
Published in:Algebra universalis 2018-09, Vol.79 (3), p.1-21, Article 66
Main Author: Citkin, Alex
Format: Article
Language:English
Subjects:
Algebra
Congruences
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its homomorphic image. Using this criterion of projectivity, we describe the primitive subquasivarieties of discriminator varieties that have a finite minimal algebra embedded in every nontrivial algebra from this variety. In particular, we describe the primitive quasivarieties of discriminator varieties of monadic Heyting algebras, Heyting algebras with regular involution, Heyting algebras with a dual pseudocomplement, and double-Heyting algebras.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-018-0555-3