Constructive Commutative Algebra (Record no. 58506)

000 -LEADER
fixed length control field 03706nam a22005535i 4500
001 - CONTROL NUMBER
control field 978-3-319-19494-3
003 - CONTROL NUMBER IDENTIFIER
control field DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20210120150115.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 151211s2015 gw | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783319194943
-- 978-3-319-19494-3
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.1007/978-3-319-19494-3
Source of number or code doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA251.3
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBF
Source bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code MAT002010
Source bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code PBF
Source thema
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.44
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Yengui, Ihsen.
Relator term author.
Relator code aut
-- http://id.loc.gov/vocabulary/relators/aut
245 10 - TITLE STATEMENT
Title Constructive Commutative Algebra
Medium [electronic resource] :
Remainder of title Projective Modules Over Polynomial Rings and Dynamical Gröbner Bases /
Statement of responsibility, etc. by Ihsen Yengui.
250 ## - EDITION STATEMENT
Edition statement 1st ed. 2015.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture Cham :
Name of producer, publisher, distributor, manufacturer Springer International Publishing :
-- Imprint: Springer,
Date of production, publication, distribution, manufacture, or copyright notice 2015.
300 ## - PHYSICAL DESCRIPTION
Extent VII, 271 p. 5 illus.
Other physical details online resource.
336 ## - CONTENT TYPE
Content type term text
Content type code txt
Source rdacontent
337 ## - MEDIA TYPE
Media type term computer
Media type code c
Source rdamedia
338 ## - CARRIER TYPE
Carrier type term online resource
Carrier type code cr
Source rdacarrier
347 ## - DIGITAL FILE CHARACTERISTICS
File type text file
Encoding format PDF
Source rda
490 1# - SERIES STATEMENT
Series statement Lecture Notes in Mathematics,
International Standard Serial Number 0075-8434 ;
Volume/sequential designation 2138
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Projective modules over polynomial rings -- Dynamical Gr ̈obner bases -- Syzygies in polynomial rings over valuation domains -- Exercises -- Detailed solutions to the exercises.
520 ## - SUMMARY, ETC.
Summary, etc. 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.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Commutative algebra.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Commutative rings.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical logic.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computer science—Mathematics.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Commutative Rings and Algebras.
Authority record control number https://scigraph.springernature.com/ontologies/product-market-codes/M11043
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Mathematical Logic and Foundations.
Authority record control number https://scigraph.springernature.com/ontologies/product-market-codes/M24005
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Symbolic and Algebraic Manipulation.
Authority record control number https://scigraph.springernature.com/ontologies/product-market-codes/I17052
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer Nature eBook
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9783319194950
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Printed edition:
International Standard Book Number 9783319194936
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Lecture Notes in Mathematics,
International Standard Serial Number 0075-8434 ;
Volume number/sequential designation 2138
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://doi.org/10.1007/978-3-319-19494-3">https://doi.org/10.1007/978-3-319-19494-3</a>
912 ## -
-- ZDB-2-SMA
912 ## -
-- ZDB-2-SXMS
912 ## -
-- ZDB-2-LNM
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type E-BOOKS
Holdings
Withdrawn status Lost status Damaged status Not for loan Home library Current library Date acquired Total Checkouts Barcode Date last seen Uniform Resource Identifier Price effective from Koha item type
        IMSc Library IMSc Library 20/01/2021   EBK15769 20/01/2021 https://doi.org/10.1007/978-3-319-19494-3 20/01/2021 E-BOOKS
The Institute of Mathematical Sciences, Chennai, India

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