Commutative Noetherian semigroups are finitely generated
A commutative semigroup \(S\) is called Noetherian if the set of congruences of \(S\), \(\text{Cong }S\), -- ordered in the usual way: \(\sim\leq\sim'\) if and only if \(x\sim y\) implies \(x\sim'y\), whenever \(x,y\in S\) -- is so that is every nonempty subset of \(\text{Cong }S\) has a maximal element. The author gives a short proof of the known fact that if \(S\) is Noetherian, then \(S\) is finitely generated.
scientific article; zbMATH DE number 1889245