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Skew PBW Extensions = Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Skew PBW Extensions/ by William Fajardo, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, Helbert Venegas.
其他題名:	Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /
作者:	Fajardo, William.
其他作者:	Gallego, Claudia.
面頁冊數:	XV, 584 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Associative rings. -
電子資源:	https://doi.org/10.1007/978-3-030-53378-6
ISBN:	9783030533786

Skew PBW Extensions = Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /
Fajardo, William.

Skew PBW ExtensionsRing and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /[electronic resource] :by William Fajardo, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, Helbert Venegas. - 1st ed. 2020. - XV, 584 p.online resource. - Algebra and Applications,281572-5553 ;. - Algebra and Applications,20.

Preface -- I Ring and Module-Theoretic Properties of Skew PBW Extensions -- II Projective Modules Over Skew PBW Extensions -- III Matrix and Gröbner Methods for Skew PBW Extensions -- IV Applications: The Noncommutative AlgebraicGeometry of Skew PBW Extensions -- References.

This monograph is devoted to a new class of non-commutative rings, skew Poincaré–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 Gröbner 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.

ISBN: 9783030533786

Standard No.: 10.1007/978-3-030-53378-6doiSubjects--Topical Terms:

893564
Associative rings.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Skew PBW Extensions = Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /
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