Journal article
Agreeable domains
Communications in Algebra, Vol.23(13), pp.4861-4883
01/01/1995
DOI: 10.1080/00927879508825505
Abstract
An integral domain D with quotient field K is defined to be agreeable if for each fractional ideal F of D[X] with F C K[X] there exists 0 = s ε D with sF C D[X]. D is agreeable ⇔ D satisfies property (*) (for 0 ^ f(X) G K[X], there exists 0 = s ε D so that f(X)g(X) ε D[X] for g(X) ε K[X] implies that sg(X) ε D[X]) & D[X] is an almost principal domain, i.e., for each nonzero ideal I of D[X] with IK[X] = K[X], there exists f(X) ε I and 0 = s ε D with sI C (f(X)). If D is Noetherian or integrally closed, then D is agreeable. A number of other characterizations of agreeable domains are given as are a number of stability properties. For example, if D is agreeable, so is ⋂ α D P α and for a pair of domains D⊆D′ with a [DD:′]≠0, D is agreeable⇔D′ is agreeable. Results on agreeable domains are used to give an alternative treatment of Querre's characterization of divisorial ideals in integrally closed polynomial rings. Finally, the various characterizations of D being agreeable are considered for polynomial rings in several variables.
Details
- Title: Subtitle
- Agreeable domains
- Creators
- D.D Anderson - Department of Mathematics , The University of IowaDong Je Kwak - Department of Mathematics , The University of IowaMuhammad Zafrullah - Department of Mathematics , The University of Iowa
- Resource Type
- Journal article
- Publication Details
- Communications in Algebra, Vol.23(13), pp.4861-4883
- Publisher
- Marcel Dekker, Inc
- DOI
- 10.1080/00927879508825505
- ISSN
- 0092-7872
- eISSN
- 1532-4125
- Language
- English
- Date published
- 01/01/1995
- Academic Unit
- Mathematics
- Record Identifier
- 9983986099102771
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