| Description |
1 online resource (xi, 820 pages) |
| Series |
Encyclopedia of mathematics and its applications ; 158 |
|
Encyclopedia of mathematics and its applications ; 158.
|
| Contents |
Zacharias -- Bergman -- Ufnarovski -- Weispfenning -- Spear 2 -- Weispfenning II -- Sweedler -- Hironaka -- Hironaka II -- Janet -- Macaulay V -- Gerdt and Faugere |
| Summary |
In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers |
| Bibliography |
Includes bibliographical references (pages 803-812) and index |
| Notes |
Print version record |
| Subject |
Commutative rings.
|
|
Commutative algebra.
|
|
MATHEMATICS -- Algebra -- Intermediate.
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Anillos conmutativos
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Álgebra conmutativa
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Commutative algebra
|
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Commutative rings
|
| Form |
Electronic book
|
| ISBN |
9781316271902 |
|
1316271900 |
|
9781316384985 |
|
1316384985 |
|
