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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 toolsof 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.
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 toolsof 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.
Presents a new point of view concerning problems in Commutative Algebra and Algebraic Geometry
All the proofs are constructive (algorithms) and simple
The reader can easily implement the presented algorithms in his preferred Computer Algebra System
Projective modules over polynomial rings.- Dynamical Gr¿obner bases.- Syzygies in polynomial rings over valuation domains.- Exercises.- Detailed solutions to the exercises.
| Erscheinungsjahr: | 2015 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 284 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
vii
271 S. 5 s/w Illustr. 271 p. 5 illus. |
| ISBN-13: | 9783319194936 |
| ISBN-10: | 3319194933 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-19493-6 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Yengui, Ihsen |
| Auflage: | 1st ed. 2015 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 16 mm |
| Von/Mit: | Ihsen Yengui |
| Erscheinungsdatum: | 12.12.2015 |
| Gewicht: | 0,435 kg |
Presents a new point of view concerning problems in Commutative Algebra and Algebraic Geometry
All the proofs are constructive (algorithms) and simple
The reader can easily implement the presented algorithms in his preferred Computer Algebra System
Projective modules over polynomial rings.- Dynamical Gr¿obner bases.- Syzygies in polynomial rings over valuation domains.- Exercises.- Detailed solutions to the exercises.
| Erscheinungsjahr: | 2015 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 284 |
| Reihe: | Lecture Notes in Mathematics |
| Inhalt: |
vii
271 S. 5 s/w Illustr. 271 p. 5 illus. |
| ISBN-13: | 9783319194936 |
| ISBN-10: | 3319194933 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-19493-6 |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Yengui, Ihsen |
| Auflage: | 1st ed. 2015 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Lecture Notes in Mathematics |
| Maße: | 235 x 155 x 16 mm |
| Von/Mit: | Ihsen Yengui |
| Erscheinungsdatum: | 12.12.2015 |
| Gewicht: | 0,435 kg |
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