Displaying similar documents to “Weak alg-universality and Q -universality of semigroup quasivarieties”

On universality of semigroup varieties

Marie Demlová, Václav Koubek (2006)

Archivum Mathematicum

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A category K is called α -determined if every set of non-isomorphic K -objects such that their endomorphism monoids are isomorphic has a cardinality less than α . A quasivariety Q is called Q -universal if the lattice of all subquasivarieties of any quasivariety of finite type is a homomorphic image of a sublattice of the lattice of all subquasivarieties of Q . We say that a variety V is var-relatively alg-universal if there exists a proper subvariety W of V such that homomorphisms of V whose...

Normal cryptogroups with an associate subgroup

Mario Petrich (2013)

Czechoslovak Mathematical Journal

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Let S be a semigroup. For a , x ∈ S such that a = a x a , we say that x is an associate of a . A subgroup G of S which contains exactly one associate of each element of S is called an associate subgroup of S . It induces a unary operation in an obvious way, and we speak of a unary semigroup satisfying three simple axioms. A normal cryptogroup S is a completely regular semigroup whose ℋ -relation is a congruence and S / ℋ is a normal band. Using the representation of S as a strong semilattice of Rees matrix...

On left C - 𝒰 -liberal semigroups

Yong He, Fang Shao, Shi-qun Li, Wei Gao (2006)

Czechoslovak Mathematical Journal

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In this paper the equivalence 𝒬 ˜ U on a semigroup S in terms of a set U of idempotents in S is defined. A semigroup S is called a 𝒰 -liberal semigroup with U as the set of projections and denoted by S ( U ) if every 𝒬 ˜ U -class in it contains an element in U . A class of 𝒰 -liberal semigroups is characterized and some special cases are considered.

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...