Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
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The work Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
Resource Information
The work Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
 Title remainder
 Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
 Statement of responsibility
 by Ihsen Yengui
 Language

 eng
 eng
 Summary
 The main goal of this book is to find the constructive content hidden in abstract proofs of concrete theorems in Commutative Algebra, especially in wellknown theorems concerning projective modules over polynomial rings (mainly the QuillenSuslin theorem) and syzygies of multivariate polynomials with coefficients in a valuation ring. Simple and constructive proofs of some results in the theory of projective modules over polynomial rings are also given, and light is cast upon recent progress on the Hermite ring and Gröbner ring conjectures. New conjectures on unimodular completion arising from our constructive approach to the unimodular completion problem are presented. Constructive algebra can be understood as a first preprocessing step for computer algebra that leads to the discovery of general algorithms, even if they are sometimes not efficient. From a logical point of view, the dynamical evaluation gives a constructive substitute for two highly nonconstructive tools of abstract algebra: the Law of Excluded Middle and Zorn's Lemma. For instance, these tools are required in order to construct the complete prime factorization of an ideal in a Dedekind ring, whereas the dynamical method reveals the computational content of this construction. These lecture notes follow this dynamical philosophy
 Dewey number
 512.44
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 80n3p2yR0fs
 Image bit depth
 0
 Language note
 English
 LC call number
 QA251.3
 Literary form
 non fiction
 Series statement
 Lecture Notes in Mathematics,
 Series volume
 2138
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