The congruence extension property for algebraic semigroups
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.\}
scientific article; zbMATH DE number 4202595