Numerical semigroups with the generalized Gorenstein property Let S be a numerical semigroup and let R be its semigroup ring K[\![S]\!]. We say that S has the generalized Gorenstein property if its semigroup ring has this property. For the definition and characterization of generalized Gorenstein rings please see .

s is a numerical semigroup. The output is true if the semigroup ring K[\![S]\!] is generalized Gorenstein using the characterization by Goto-Kumashiro ().
gap> s:=NumericalSemigroup(3,7,8);; gap> IsAlmostSymmetric(s); false gap> IsGeneralizedGorenstein(s); true