Fraser–Horn–Hu property for ordered algebras

Tasić B.

Communications in Algebra, vol.50, no.5, pp.1842-1857, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1080/00927872.2021.1991939
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1842-1857
  • Keywords: Fraser-Horn-Hu property, Mal'cev conditions, ordered algebras
  • TED University Affiliated: No


© 2021 Taylor & Francis Group, LLC.Fraser and Horn, and independently Hu, studied varieties (Formula presented.) of algebras satisfying the property that for every (Formula presented.) every congruence (Formula presented.) is a product congruence, i.e., (Formula presented.) for some (Formula presented.) i = 1, 2. Varieties of rings with identity and congruence distributive varieties of algebras satisfy this property. It is easy to show that an algebra (Formula presented.) has the Fraser–Horn–Hu property if and only if the map (Formula presented.) is a lattice isomorphism from (Formula presented.) to (Formula presented.) The property was later referred to in the literature as the Fraser–Horn–Hu property. It turns out that the Fraser–Horn–Hu property is a Mal’cev condition for varieties. In this paper, we generalize this property to varieties of ordered algebras. The classic result of Fraser, Horn and Hu follows as a special case.