Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
E-disjunctive semigroups and idempotent pure congruences
Authors: R. S. Gigon
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Abstract
An equivalence relation on a semigroup S is called idempotent pure if all elements of each its class containing idempotent are idempotents, and S is said to be E-disjunctive if the identity relation is the largest idempotent pure congruence on S. We prove that an arbitrary equivalence class of the largest idempotent pure congruence on a semigroup S either consists entirely of E-inversive elements or has no E-inversive elements of S, and then that each E-disjunctive semigroup is necessarily E-inversive. Moreover, in some special classes of semigroups, which are contained in the class of E-inversive semigroups, we investigate the connections between the largest idempotent pure congruence, the least group congruence and some other relation. Basing on this, we give certain new characterizations of the least group (Clifford) congruence.Fulltext
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Contents
- On Latin squares of polynomially complete quasigroups and quasigroups generated by shifts
- Hom-Bol algebras
- Ascending chain conditions on principal left and right ideals for semidirect products of ordered semigroups
- On regular medial division algebras
- Contractions of quasigroups and Latin squares
- On 2-absorbing semimodules
- Strong forms of orthogonality for sets of frequency hypercubes
- A still shorter axiom for trimedial quasigroups
- Clifford congruences on perfect semigroups
- E-disjunctive semigroups and idempotent pure congruences
- Groups with the same orders and large character degrees as PGL(2,9)
- Coset diagrams of the action of a certain Bianchi group on PL(Fp)
- Automorphisms of abelian n-ary groups
- Free products of dimonoids
