The ideal retraction property for idempotent semigroups.
A semigroup \(S\) is said to have the `ideal retraction property' provided each of its ideals is the image of an idempotent endomorphism of \(S\). It is proved that a band \(B=[Y;S_\alpha]\) (presented as a semilattice of rectangular bands) has the ideal retraction property if and only if \(B\) is normal and \(Y\) is a tree that contains no \(\omega+1\) chain.
scientific article; zbMATH DE number 5148908