Finitely generated flat module is projective
Weba finitely generated flat ideal, projectivity is the same as having finitely generated annihilator. For rings with the weakened form of coherency that finitely generated ideals … WebJul 15, 2004 · G. Puninski, Projective modules over the endomorphism ring of a biuniform module, J. Pure Appl. Algebra, in press. On a criterion of projectivity of finitely …
Finitely generated flat module is projective
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WebJul 5, 2016 · N N is a finitely generated module, N N is a flat module. then N N is a free module. This is Matsumara, Theorem 7.10. Examples. ... S. Jondrup, Flat and … WebPDF On Apr 1, 1969, Wolmer V. Vasconcelos published On Finitely Generated Flat Modules Find, read and cite all the research you need on ResearchGate ... flat module is projective, R is a ...
WebSep 9, 2024 · Similarly, if projectiveness was a local property, then every finitely generated flat module would be a projective module). Recall that for a given ring R , the collection of subsets \(D(f)\cap V(I)\) with \(f\in R\) and I runs through the set of finitely generated ideals of R forms a basis for the opens of the patch topology over \({\text ... Web38.12 Flat finitely presented modules. 38.12. Flat finitely presented modules. In some cases given a ring map of finite presentation and a finitely presented -module the …
WebApr 6, 2024 · In this article, the projectivity of finitely generated flat modules of a commutative ring are studied from a topological point of view. Then various interesting results are obtained. For instance, it is shown that if a ring has either a finitely many minimal primes or a finitely many maximal ideals then every finitely generated flat … WebThe projective dimension of a module is the shortest length of a projective resolution. 5. ... A faithfully flat module over a ring R is a flat module whose tensor product with any non-zero module is non-zero. 2. ... A finitely generated module M is called pseudo-zero if = ...
WebMar 31, 2024 · A right R-module M is called n-copure projective if Ext(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext(M, F) = 0 for all flat right R ...
Webis shown that a ring for which a projective module with finitely gen-erated localizations is always finitely generated, is precisely one of the kind mentioned above (Theorem 2.1). Such a ring R could also be characterized as "any finitely generated flat module is projective." 1. Preliminaries. mongodb schema validation arrayWebMar 24, 2024 · Using the theory of 1‐minimal models, we also show that a finitely generated group π admits a connected 1‐model with finite‐dimensional degree 1 piece if and only if the… Show more mongodb schema for chat applicationWeba finitely generated flat ideal, projectivity is the same as having finitely generated annihilator. For rings with the weakened form of coherency that finitely generated ideals … mongodb scriptingWebfrom which it follows S=(0). This shows that M is a finitely generated flat module of constant rank and it then follows (e.g. [8]) that it is projective. 2. The annihilator of a flat module. Annihilators of arbitrary flat modules can be wild as for any nondomain A "most" localizations A-^AS ([5] has several mongodb search by objectidWeb10.83. Descent for finite projective modules. In this section we give an elementary proof of the fact that the property of being a finite projective module descends along faithfully flat ring maps. The proof does not apply when we drop the finiteness condition. However, the method is indicative of the one we shall use to prove descent for the ... mongodb search dateWebOct 15, 2024 · Similarly, it is known that finitely presented flat modules are projective, but only over coherent rings, do we know that all finitely presented Gorenstein flat modules are Gorenstein projective [3, Proposition 1.3], and whether it is true or not in general case still remains open. Moreover, it is well known that all flat modules are projective ... mongodb search by nameWebOver a general ring (not necessarily commutative), every finitely presented flat module is projective. So, one simple condition on the ring that gives you what you want is that every finitely generated module is finitely presented. Of course, these are just the (left) Noetherian rings. Share. Cite. Improve this answer. mongodb search in a list