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Skew PBW extensionsring and module-t...

Fajardo, William.

Skew PBW extensionsring and module-theoretic properties, matrix and Grobner methods, and applications /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Skew PBW extensionsby William Fajardo ... [et al.].
Reminder of title:	ring and module-theoretic properties, matrix and Grobner methods, and applications /
other author:	Fajardo, William.
Published:	Cham :Springer International Publishing :2020.
Description:	xv, 584 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Noncommutative rings.
Online resource:	https://doi.org/10.1007/978-3-030-53378-6
ISBN:	9783030533786$q(electronic bk.)

Skew PBW extensionsring and module-theoretic properties, matrix and Grobner methods, and applications /
Skew PBW extensionsring and module-theoretic properties, matrix and Grobner methods, and applications /[electronic resource] :by William Fajardo ... [et al.]. - Cham :Springer International Publishing :2020. - xv, 584 p. :ill., digital ;24 cm. - Algebra and applications,v.281572-5553 ;. - Algebra and applications ;v.17..

Preface -- I Ring and Module-Theoretic Properties of Skew PBW Extensions -- II Projective Modules Over Skew PBW Extensions -- III Matrix and Grobner 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 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 Grobner 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$q(electronic bk.)

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

573190
Noncommutative rings.

LC Class. No.: QA251.4

Dewey Class. No.: 512.46

Skew PBW extensionsring and module-theoretic properties, matrix and Grobner methods, and applications /
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245 0 0 $a Skew PBW extensions $h [electronic resource] : $b ring and module-theoretic properties, matrix and Grobner methods, and applications / $c by William Fajardo ... [et al.].
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490 1 $a Algebra and applications, $x 1572-5553 ; $v v.28
505 0 $a Preface -- I Ring and Module-Theoretic Properties of Skew PBW Extensions -- II Projective Modules Over Skew PBW Extensions -- III Matrix and Grobner Methods for Skew PBW Extensions -- IV Applications: The Noncommutative AlgebraicGeometry of Skew PBW Extensions -- References.
520 $a 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 Grobner 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.
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650 0 $a Algorithms. $3 184661
650 1 4 $a Associative Rings and Algebras. $3 274818
650 2 4 $a Category Theory, Homological Algebra. $3 275954
700 1 $a Fajardo, William. $3 883096
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