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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