Constructive commutative algebra: projective modules over polynomial rings and dynamical Gröbner bases
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2015]
|
| Schriftenreihe: | Lecture Notes in Mathematics
2138 |
| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online Ressource (VII, 271 Seiten, 5 illus) |
| ISBN: | 9783319194943 9783319194936 |
| ISSN: | 0075-8434 |
| DOI: | 10.1007/978-3-319-19494-3 |
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Datensatz im Suchindex
| _version_ | 1804175846571769856 |
|---|---|
| adam_text | CONSTRUCTIVE COMMUTATIVE ALGEBRA
/ YENGUI, IHSEN
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
PROJECTIVE MODULES OVER POLYNOMIAL RINGS
DYNAMICAL GR¨OBNER BASES
SYZYGIES IN POLYNOMIAL RINGS OVER VALUATION DOMAINS
EXERCISES
DETAILED SOLUTIONS TO THE EXERCISES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
CONSTRUCTIVE COMMUTATIVE ALGEBRA
/ YENGUI, IHSEN
: 2015
ABSTRACT / INHALTSTEXT
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 GROEBNER 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
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Yengui, Ihsen 1972- |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-19494-3 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:22:47Z |
| institution | BVB |
| isbn | 9783319194943 9783319194936 |
| issn | 0075-8434 |
| language | English |
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| spelling | Yengui, Ihsen 1972- Verfasser (DE-588)1082016144 aut Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases Ihsen Yengui Cham Springer [2015] © 2015 1 Online Ressource (VII, 271 Seiten, 5 illus) txt rdacontent c rdamedia cr rdacarrier Lecture notes in mathematics 2138 0075-8434 Mathematics Computer science / Mathematics Commutative algebra Commutative rings Mathematical logic Commutative Rings and Algebras Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Informatik Mathematik Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s DE-604 Lecture Notes in Mathematics 2138 (DE-604)BV014303148 2138 https://doi.org/10.1007/978-3-319-19494-3 Verlag URL des Erstveröffentlichers Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730276&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Yengui, Ihsen 1972- Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases Lecture Notes in Mathematics Mathematics Computer science / Mathematics Commutative algebra Commutative rings Mathematical logic Commutative Rings and Algebras Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Informatik Mathematik Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4164821-3 |
| title | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases |
| title_auth | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases |
| title_exact_search | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases |
| title_full | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases Ihsen Yengui |
| title_fullStr | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases Ihsen Yengui |
| title_full_unstemmed | Constructive commutative algebra projective modules over polynomial rings and dynamical Gröbner bases Ihsen Yengui |
| title_short | Constructive commutative algebra |
| title_sort | constructive commutative algebra projective modules over polynomial rings and dynamical grobner bases |
| title_sub | projective modules over polynomial rings and dynamical Gröbner bases |
| topic | Mathematics Computer science / Mathematics Commutative algebra Commutative rings Mathematical logic Commutative Rings and Algebras Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Informatik Mathematik Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Mathematics Computer science / Mathematics Commutative algebra Commutative rings Mathematical logic Commutative Rings and Algebras Mathematical Logic and Foundations Symbolic and Algebraic Manipulation Informatik Mathematik Kommutative Algebra |
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