Titlebook: Commutative Algebra: Constructive Methods; Finite Projective Mo Henri Lombardi,Claude Quitté Book 2015 Springer Science+Business Media Dord

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Finitely Presented Modules,esented modules is a slightly more abstract, and at times more profitable, way to approach the subject of systems of linear equations. We provide the basics of the theory of finitely presented modules. We treat the examples of finitely presented modules over PIDs, over Bezout rings and over zero-dim

interlude

Cuisine

弓箭

Finitely Generated Projective Modules, 2, of finitely generated projective modules as locally free modules. Section?. is dedicated to an elementary theory of the rank which does not require prime ideals. In Sect.?. we give some simple applications of the local structure theorem. Section?. is an introduction to Grassmannians. In Sect.?. we

Tremor

The Number of Generators of a Module,due in their original version to Kronecker, Bass, Serre, Forster and Swan, regard the number of radical generators of a finitely generated ideal, the number of generators of a module, the possibility of producing a free submodule as a direct summand in a module, and the possibility of simplifying is

Tremor

The Local-Global Principle,due in their original version to Kronecker, Bass, Serre, Forster and Swan, regard the number of radical generators of a finitely generated ideal, the number of generators of a module, the possibility of producing a free submodule as a direct summand in a module, and the possibility of simplifying is

rods366

Extended Projective Modules,e extended from the base ring. We especially treat Traverso-Swan’s theorem (rank one projective modules over R[X] are extended if and only if R is seminormal), the patching á la Vaserstein-Quillen, Horrocks’ theorems, Quillen-Suslin’s theorem, Bass theorem (finitely generated projective modules over

蕨類

Finitely Generated Projective Modules, 2,introduce the fundamental and difficult problem of classifying finitely generated projective modules over a fixed ring. Section?. presents a nontrivial example for which this classification can be obtained.

Essential

The Number of Generators of a Module,omorphisms. Decisive progress was made by R. Heitmann who proved how to get rid of Noetherian hypotheses. Further progress was made by T. Coquand who proved how to obtain all the results, sometimes in a stronger form, by constructive and elementary proofs.