The congruence lattice of a regular semigroup

DOI10.1016/0022-4049(88)90015-1zbMath0649.20052OpenAlexW1986212867MaRDI QIDQ1105702

Francis Pastijn, Mario Petrich

Publication date: 1988

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(88)90015-1

zbMATH Keywords

idempotentsrectangular bandscompletely simple semigroupscongruence latticesubdirect decompositionregular semigroupleft groupsright groupsidempotent-separatingcomplete congruence

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Subalgebras, congruence relations (08A30) Mappings of semigroups (20M15)

Related Items (27)

The Green relations approach to congruences on completely regular semigroups ⋮ On congruence lattices of regular semigroups with \(Q\)-inverse transversals ⋮ Pseudovarieties of completely regular semigroups ⋮ Commutativity of operators on the lattice of existence varieties ⋮ The \(\mathcal K^\circ\)-relation on the congruence lattice of a regular semigroup with an inverse transversal. ⋮ Operators and products in the lattice of existence varieties of regular semigroups ⋮ On existence varieties of locally inverse semigroups ⋮ A method for the construction of complete congruences on lattices of pseudovarieties ⋮ Homomorphisms and Congruences of Medial Semigroups with an Associate Subgroup ⋮ Congruence lattices of algebras— the signed labelling ⋮ Relationships among quasivarieties induced by the min networks on inverse semigroups ⋮ Complete endomorphisms of the lattice of pseudovarieties of finite semigroups ⋮ Some special congruences on completely regular semigroups ⋮ Congruence Networks on Regular Semigroups Associated with 𝒱-Relation ⋮ Congruences on abundant semigroups associated with {G}reen's \(*\)-relations ⋮ SEMIGROUPS OF OPERATORS ASSOCIATED WITH THE KERNEL AND TRACE OF CONGRUENCES ON E-UNITARY COMPLETELY REGULAR SEMIGROUPS ⋮ STRONGLY ORTHODOX CONGRUENCES ON AN -INVERSIVE SEMIGROUP ⋮ Congruence lattices of regular semigroups with inverse transversals¹ ⋮ \(E\omega\)-Clifford congruences and \(E\omega\)-\(E\)-reflexive congruences on an inverse semigroup. ⋮ The congruence lattice of a strict regular semigroup ⋮ On the congruence extension property for semigroups: preservation under homomorphic images ⋮ COMPLETE LATTICE HOMOMORPHISM OF STRONGLY REGULAR CONGRUENCES ON -INVERSIVE SEMIGROUPS ⋮ Complete Congruences on Lattices of Varieties and of Pseudovarieties ⋮ Orthodox semigroups with complemented congruence lattices ⋮ Some remarkable congruences on completely regular semigroups ⋮ Associativity of products of existence varieties of regular semigroups ⋮ R-Unipotent Congruences on Eventually Regular Semigroups

Cites Work

• Joins and meets of congruences on a regular semigroup
• Lattices of completely regular semigroup varieties
• Regular semigroup congruences
• Congruences on an orthodox semigroup via the minimum inverse semigroup congruence
• Congruences on Regular Semigroups
• Structure of regular semigroups. I
• The natural partial order on a regular semigroup
• Decompositions of the congruence lattice of a semigroup
• Coextensions of Regular Semigroups by Rectangular Bands.I
• The lattice of congruences on a band of groups
• Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups
• On regular semigroups whose idempotents form a subsemigroup
• On the lattice of congruences on a regular semigroup
• Congruences and Green's relations on regular semigroups

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