w-Divisoriality in Polynomial Rings

Details w-Divisoriality in Polynomial Rings w-Divisoriality in Polynomial Rings

2008-07-21

arxiv.org/abs/0807.3299v1

Mathematics

Commutative Algebra

9 pages Comm. Algebra

Scientific paper

We extend the Bass-Matlis characterization of local Noetherian divisorial
domains to the non-Noetherian case. This result is then used to study the
following question: If a domain D is w-divisorial, that is, if each w-ideal of
D is divisorial, then is D[X] automatically w-divisorial? We show that the
answer is yes if D is either integrally closed or Mori.

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