Publication at Faculty of Mathematics and Physics |
2011
Abstract
A variety V is var- relatively universal if it contains a subvariety W such that the class of all homomorphisms that do not factorize through any algebra in W is algebraically universal. And V has an algebraically universal alpha - expansion alpha V if adding a nullary operations to all algebras in V gives rise to a class alpha V of algebras that is algebraically universal.
The first two authors have conjectured that any varrelative universal variety V has an algebraically universal alpha- expansion aV. This note contains a more general result that proves this conjecture.