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On universality of semigroup varieties

Marie Demlová, Václav Koubek (2006)

Archivum Mathematicum

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 image does...

On V n -semigroups

Ze Gu, Xilin Tang (2015)

Open Mathematics

In this paper, we give some new characterizations of orthodox semigroups in terms of the set of inverses of idempotents. As a generalization, a new class of regular semigroups, namely Vn-semigroups, is introduced. Also, we give a characterization of Vn-semigroups and investigate some properties of Vn-semigroups. Furthermore, we show that the class of Vn-semigroups is closed under direct products and homomorphic images. However, regular subsemigroups of Vn-semigroups (n ≥ 2) are not necessarily Vn-semigroups...

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