Title: A note on homomorphisms between products of algebras
Language: English
Authors: Chajda, Ivan
Goldstern, Martin
Länger, Helmut
Category: Research Article
Issue Date: 2018
Journal: Algebra universalis
ISSN: 0002-5240
Let K be a congruence distributive variety and call an algebra hereditarily directly irreducible (HDI) if every of its subalgebras is directly irreducible. It is shown that every homomorphism from a finite direct product of arbitrary algebras from K to an HDI algebra from K is essentially unary. Hence, every homomorphism from a finite direct product of algebras Ai (i∈I) from K to an arbitrary direct product of HDI algebras Cj (j∈J) from K can be expressed as a product of homomorphisms from Aσ(j) to Cj for a certain mapping σ from J to I. A homomorphism from an infinite direct product of elements of K to an HDI algebra will in general not be essentially unary, but will always factor through a suitable ultraproduct.
Keywords: Direct product of chains; Homomorphism; Essentially unary mapping; Ultrafilter
DOI: 10.1007/s00012-018-0517-9
Library ID: AC15324293
URN: urn:nbn:at:at-ubtuw:3-5158
Organisation: E104 - Institut für Diskrete Mathematik und Geometrie 
Publication Type: Article
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