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We call a semigroup $S$ f-noetherian if every right congruence of finiteindex on $S$ is finitely generated. We prove that every finitely generatedsemigroup is f-noetherian, and investigate whether the properties of beingf-noetherian and being finitely generated coincide for various semigroupclasses.

Semigroups for which every right congruence of finite index is finitely generated