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Proprietes et applications de la notion de contenu

 

作者: Gabriel Picavet,  

 

期刊: Communications in Algebra  (Taylor Available online 1985)
卷期: Volume 13, issue 10  

页码: 2231-2265

 

ISSN:0092-7872

 

年代: 1985

 

DOI:10.1080/00927878508823275

 

出版商: Gordon and Breach Science Publishers Ltd.

 

数据来源: Taylor

 

摘要:

The notion of content is used to solve certain problems. In the first part, we show that the structural morphism of a content algebra (see the paper of D.E. Rush [22] ) is spectrally open, under mild hypothesis. We show also that a flat module is universally content if and only if it is a Mittag-Leffler’s module in the sense of f2ll . In the second part, using content, we exhibit a kind of localization of a commutative ring A, attached to eyery subset X of Spec(A) i.e. a flat morphism A→ X(A). We can thus show that every quasi-compact, stable under generization subset of a spectra is a spectral image under a flat morphism, in a canonical way. We can also give in certain cases an elementary construction of the maximal flat injective epimor-phism of a ring. Suppose that A is a Noetherian ring and consider pro-perties of Noetherian rings such as factoriality, normality and so on.

 

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