株式会社極東書店トップ ＞ 商品一覧 ＞ Skew PBW Extensions : Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications. 1st ed. 2020.
商品詳細
Skew PBW Extensions : Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications. 1st ed. 2020.
・ISBN 978-3-030-53377-9 hard EUR 129.99
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| 著者・編者 | Fajardo, William / Gallego, Claudia / Lezama, Oswaldo / Reyes, Armando / Suarez, Hector / Venegas, Helbert, |
|---|---|
| シリーズ | Algebra and Applications |
| 出版社 | (Springer Nature Switzerland AG, SZ) |
| 出版年月 | 2020 |
| ページ数 | 584 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-4675＞ |
解説
This monograph is devoted to a new class of non-commutative rings, skew Poincare-Birkhoff-Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Groebner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin-Schelter regular algebras, and the noncommutative Zariski cancellation problem.
The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.