Topic
Epigroup
About: Epigroup is a research topic. Over the lifetime, 31 publications have been published within this topic receiving 88 citations. The topic is also known as: quasi-periodic semigroup & group-bound semigroup.
Papers
TL;DR: It is shown that there exists an order preserving embedding of the lattICE of complete congruences on the lattice Lp(P) of all subpseudovarieties of a given pseudovariety P into the direct product of the latices of completeCongruencesOn lattices of subvarieties of varieties generated by members of P.
Abstract: Three methods for the construction of all complete congruences on the lattice Lv(V) of subvarieties of a variety V are introduced. It is shown that there exists an order preserving embedding of the lattice of complete congruences on the lattice Lp(P) of all subpseudovarieties of a given pseudovariety P into the direct product of the lattices of complete congruences on lattices of subvarieties of varieties generated by members of P; thus there are methods for constructing all complete congruences on Lp(P). By way of application, 2ℵ0 complete congruences and complete endomorphisms are constructed on any lattice Lv(V), where V is a certain epigroup variety which includes all bands; there is an analogous application for the lattice of all pseudovarieties of semigroups.
12 citations
TL;DR: In this article, the structure of an epigroup with upper semimodular subepigroup lattice is described modulo groups, and certain properties of epigroups are invariant under taking a lattice-isomorphic epigroup.
Abstract: The structure of an epigroup with upper semimodular subepigroup lattice is described modulo groups. A special case is distinguished when this lattice belongs to a quasivariety contained in the variety of all modular lattices. It is also shown that certain properties of epigroups are invariant under taking a lattice isomorphic epigroup; this takes place, in particular, for epigroups decomposable into a semilattice of archimedean epigroups and for some types of archimedean epigroups.
9 citations
TL;DR: In this article, all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semi-girders are determined, and all the semigroup varieties are characterized.
Abstract: We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.
8 citations
25 Jul 2014
6 citations
TL;DR: In this article, several characterizations of epigroups mentioned in the title of this paper are presented. But the purpose of the paper is not to find several characterisations of the epigrams mentioned in this paper.
Abstract: The purpose of the paper is to find several characterizations of epigroups mentioned in the title. Some special cases are also considered.
6 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 2 |
| 2018 | 4 |
| 2016 | 5 |
| 2015 | 3 |
| 2014 | 4 |
| 2013 | 4 |