Semigroups with the ideal extension property
A semigroup \(S\) is said to have the ideal extension property if for each subsemigroup \(T\) of \(S\) and an ideal \(I\) of \(T\), there exists an ideal \(J\) of \(S\) such that \(J\cap T=I\). It is proved that \(S\) has this property if and only if \(S\) is a semilattice of ideal extensions of completely simple semigroups over torsion groups that satisfy three additional conditions involving the regular members of \(S\). Particular cases then give some crisp results: for instance a regular semigroup has the ideal extension property if and only if \(S\) is a completely regular semigroup each of whose maximum subgroups is a torsion group.
scientific article; zbMATH DE number 1985875