Agreeable domains
作者:
D.D. Anderson,
Dong Je Kwak,
Muhammad Zafrullah,
期刊:
Communications in Algebra
(Taylor Available online 1995)
卷期:
Volume 23,
issue 13
页码: 4861-4883
ISSN:0092-7872
年代: 1995
DOI:10.1080/00927879508825505
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
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 ⋂αDPαand 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.
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