Hereditarily finitely generated commutative monoids (Q1965269)

A commutative monoid \(S\) is said to be an HFG monoid (for hereditarily finitely generated) if each submonoid of \(S\) is finitely generated. In this paper, the authors characterize when \(F/\sigma\) is an HFG monoid, where \(\sigma\) is a congruence on a finitely generated commutative free monoid \(F\). They also give an algorithm to determine, from a presentation of \(\sigma\), when \(F/\sigma\) is an HFG monoid. These results are then applied to the case where \(F/\sigma\) is a cancellative HFG monoid.