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Equimorphy in varieties of distributive double p -algebras

Václav KoubekJiří Sichler — 1998

Czechoslovak Mathematical Journal

Any finitely generated regular variety 𝕍 of distributive double p -algebras is finitely determined, meaning that for some finite cardinal n ( 𝕍 ) , any subclass S 𝕍 of algebras with isomorphic endomorphism monoids has fewer than n ( 𝕍 ) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p -algebras...

Weak alg-universality and Q -universality of semigroup quasivarieties

Marie DemlováVáclav Koubek — 2005

Commentationes Mathematicae Universitatis Carolinae

In an earlier paper, the authors showed that standard semigroups 𝐌 1 , 𝐌 2 and 𝐌 3 play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by 𝐌 2 and 𝐌 3 are neither relatively alg-universal nor Q -universal, while there do exist finite semigroups 𝐒 2 and 𝐒 3 generating the same semigroup variety as 𝐌 2 and 𝐌 3 respectively and the quasivarieties generated by 𝐒 2 and/or 𝐒 3 are quasivar-relatively f f -alg-universal and Q -universal...

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