Duality on value semigroups. (English) Zbl 1409.14050

Summary: We establish a combinatorial counterpart of the Cohen-Macaulay duality on a class of curve singularities which includes algebroid curves. For such singularities the value semigroup and the value semigroup ideals of all fractional ideals satisfy axioms that define so-called good semigroups and good semigroup ideals. We prove that each good semigroup admits a canonical good semigroup ideal which gives rise to a duality on good semigroup ideals. We show that the Cohen-Macaulay duality and our good semigroup duality are compatible under taking values.


14H20 Singularities of curves, local rings
13C14 Cohen-Macaulay modules
20M12 Ideal theory for semigroups
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