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Anti-archimedean rings and power series rings

 

作者: D.D. Anderson,   B.G. Kang,   M H. Park,  

 

期刊: Communications in Algebra  （Taylor Available online 1998）
卷期: Volume 26, issue 10  

页码: 3223-3238

 

ISSN:0092-7872

 

年代: 1998

 

DOI:10.1080/00927879808826338

 

出版商: Gordon and Breach Science Publishers Ltd.

 

关键词: Anti-Archimedean domain;SFT Prüfer domain;regular local ring;Krull domain;power series ring;valuation domain

 

数据来源: Taylor

 

摘要:

We define an integral domainDto be anti-Archimedean if. For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show thatDis anti-Archimedeanis quasilocal and in this caseis actually ann-dimensional regular local ring. We also show that ifDis an SFT Prüfer domain, thenis a Krull domain for any set of indeterminates {Xα}.

 

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