Generalized factorial ideals

الملخص EN

Using the notion of v-ordering in discrete valuation domains, Bhargava introduced factorial ideals associated with subsets of Dedekind domains, which generalize the classical factorials.

We show how v-orderings may be extended to subsets of rank-one valuation domains, and also, how factorial ideals may be generalized to subsets of Krull domains with almost the same properties.

In addition, we obtain results concerning the asymptotic behavior of the sequence of these factorial ideals.

1991 Mathematics Subject Classification.

Primary: 11B65, 13F20; Secondary: 11B83, 13F30.