The Resource Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases, by Ihsen Yengui, (electronic resource)

Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases, by Ihsen Yengui, (electronic resource)

Label
Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
Title
Constructive Commutative Algebra
Title remainder
Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases
Statement of responsibility
by Ihsen Yengui
Creator
Contributor
Author
Provider
Subject
Language
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 well-known theorems concerning projective modules over polynomial rings (mainly the Quillen-Suslin 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
Member of
http://library.link/vocab/creatorName
Yengui, Ihsen
Image bit depth
0
LC call number
QA251.3
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
2138
http://library.link/vocab/subjectName
  • Mathematics
  • Computer science
  • Commutative algebra
  • Commutative rings
  • Mathematical logic
  • Mathematics
  • Commutative Rings and Algebras
  • Mathematical Logic and Foundations
  • Symbolic and Algebraic Manipulation
Label
Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases, by Ihsen Yengui, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Projective modules over polynomial rings -- Dynamical Gr ̈obner bases -- Syzygies in polynomial rings over valuation domains -- Exercises -- Detailed solutions to the exercises
Dimensions
unknown
Extent
VII, 271 p. 5 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319194943
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-19494-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-19494-3
Label
Constructive Commutative Algebra : Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases, by Ihsen Yengui, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Projective modules over polynomial rings -- Dynamical Gr ̈obner bases -- Syzygies in polynomial rings over valuation domains -- Exercises -- Detailed solutions to the exercises
Dimensions
unknown
Extent
VII, 271 p. 5 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319194943
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-19494-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-19494-3

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