Article
Semilattice sums of algebras and Mal’tsev products of varieties
Algebra universalis
Document Type
Article
Disciplines
- Algebra and
- Mathematics
Publication Version
Accepted Manuscript
Publication Date
5-20-2020
DOI
10.1007/s00012-020-00656-8
Abstract
The Mal’tsev product of two varieties of similar algebras is always a quasivariety. We consider when this quasivariety is a variety. The main result shows that if V is a strongly irregular variety with no nullary operations, and S is a variety, of the same type as V, equivalent to the variety of semilattices, then the Mal’tsev product V ◦ S is a variety. It consists precisely of semilattice sums of algebras in V. We derive an equational basis for the product from an equational basis for V. However, if V is a regular variety, then the Mal’tsev product may not be a variety. We discuss examples of various applications of the main result, and examine some detailed representations of algebras in V ◦ S.
Copyright Owner
Springer Nature Switzerland AG
Copyright Date
2020
Language
en
File Format
application/pdf
Citation Information
Clifford Bergman, T. Penza and A. B. Romanowska. "Semilattice sums of algebras and Mal’tsev products of varieties" Algebra universalis Vol. 81 (2020) p. 33 Available at: http://works.bepress.com/clifford_bergman/16/
This is a post-peer-review, pre-copyedit version of an article published in Algebra universalis. The final authenticated version is available online at DOI: 10.1007/s00012-020-00656-8. Posted with permission.