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, Groebner 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 Faugere (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.
Reihe
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Illustrationen
Worked examples or Exercises; 40 Line drawings, unspecified
Maße
Höhe: 240 mm
Breite: 161 mm
Dicke: 53 mm
Gewicht
ISBN-13
978-1-107-10963-6 (9781107109636)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Teo Mora is a Professor of Algebra in the Department of Mathematics at the University of Genoa.
Autor*in
University of Genoa
Part VII. Beyond: 46. Zacharias; 47. Bergman; 48. Ufnarovski; 49. Weispfenning; 50. Spear2; 51. Weispfenning II; 52. Sweedler; 53. Hironaka; 54. Hironaka II; 55. Janet; 56. Macaulay V; 57. Gerdt and Faugere; Bibliography; Index.
