The congruence extension property for algebraic semigroups
type: Item
instance of: scholarly article
title: The congruence extension property for algebraic semigroups
zbMATH Open document ID: 0728.20052
DOI: 10.1007/BF02574246
author: Josefa I. Garcia
published in: Semigroup Forum
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135090
review text: An algebra A has the congruence extension property (CEP) if each congruence relation on each subalgebra extends to a congruence on A. CEP plays an important role in the study of amalgamation and related properties. \textit{B. Biró, E. W. Kiss} and \textit{P. Pálfy} [in Universal Algebra, Colloq. Math. Soc. János Bolyai 29, 129-151 (1982; Zbl 0483.08005), wrongly referenced in the paper] determined which varieties of semigroups have CEP, in the sense that they consist of semigroups with CEP. But characterization of CEP for individual semigroups remains open. The paper under review provides some necessary conditions and a few sufficient ones. For instance, a rectangular group has CEP if and only if its maximal subgroups do (considered as semigroups). \{Reviewer's remark. (1) The first open question has a negative answer. (2) The ``semigroup'' of Example 3.3 is not associative. However, a later example fulfils its role.\}
reviewed by: Peter R. Jones
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 4202595
zbMATH Keywords: congruence extension property
zbMATH Keywords: varieties of semigroups
zbMATH Keywords: semigroups with CEP
MaRDI profile type: Publication
cites work: Q3848243
cites work: A note on the congruence extension property
cites work: Extending Congruences on Semigroups
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description: scientific article; zbMATH DE number 4202595