Algebra universalis

, Volume 65, Issue 2, pp 179–184 | Cite as

Relative universality and universality obtained by adding constants



A variety \({\mathbb{V}}\) is var-relatively universal if it contains a subvariety \({\mathbb{W}}\) such that the class of all homomorphisms that do not factorize through any algebra in \({\mathbb{W}}\) is algebraically universal. And \({\mathbb{V}}\) has an algebraically universal α-expansion \({\alpha\mathbb{V}}\) if adding α nullary operations to all algebras in \({\mathbb{V}}\) gives rise to a class \({\alpha\mathbb{V}}\) of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety \({\mathbb{V}}\) has an algebraically universal α-expansion \({\alpha\mathbb{V}}\) . This note contains a more general result that proves this conjecture.

2010 Mathematics Subject Classification


Keywords and phrases

alg-universality relative alg-universality α-expansion 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Marie Demlová
    • 1
  • Václav Koubek
    • 2
  • Jiří Sichler
    • 3
  1. 1.Department of Mathematics, Faculty of Electrical EngineeringCzech Technical UniversityPraha 6Czech Republic
  2. 2.Department of Theoretical Computer Science and Mathematical Logic and Institute of Theoretical Computer Science, Faculty of Mathematics and PhysicsCharles UniversityPraha 1Czech Republic
  3. 3.Department of MathematicsUniversity of ManitobaWinnipegCanada

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