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A principal ideal theorem analogue for modules over commutative rings

 

作者: Seleena M. George,   Roy L. McCasland,   Patrick F. Smith,  

 

期刊: Communications in Algebra  （Taylor Available online 1994）
卷期: Volume 22, issue 6  

页码: 2083-2099

 

ISSN:0092-7872

 

年代: 1994

 

DOI:10.1080/00927879408824957

 

出版商: Gordon and Breach Science Publishers Ltd.

 

数据来源: Taylor

 

摘要:

The Principal Ideal Theorem states that ifReis a commutative Noetherian ring and ? is a prime ideal ofRewhich is minimal over a principal ideal thenPehas height at most 1. Also, ifReis a (not necessarily Noetherian) UFD andPeis a prime ideal ofReminimal over a principal ideal thenPehas height at most 1. We shall show that there are analogues for modules over commutative rings, but they hold only in special cases.

 

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