Displaying similar documents to “On universality of semigroup varieties”

Weak alg-universality and Q -universality of semigroup quasivarieties

Marie Demlová, Václav Koubek (2005)

Commentationes Mathematicae Universitatis Carolinae

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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...

Characterizing pure, cryptic and Clifford inverse semigroups

Mario Petrich (2014)

Czechoslovak Mathematical Journal

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An inverse semigroup S is pure if e = e 2 , a ∈ S , e < a implies a 2 = a ; it is cryptic if Green’s relation ℋ on S is a congruence; it is a Clifford semigroup if it is a semillatice of groups. We characterize the pure ones by the absence of certain subsemigroups and a homomorphism from a concrete semigroup, and determine minimal nonpure varieties. Next we characterize the cryptic ones in terms of their group elements and also by a homomorphism of a semigroup constructed in the paper. We also characterize...