國立虎尾科技大學 |

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:	Venegas, Helbert.
面頁冊數:	XV, 584 p.online resource. :
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
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:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA251.5

Dewey Class. No.: 512.46

Skew PBW Extensions = Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /
LDR:02779nam a22004095i 4500 001 1030763
003 DE-He213
005 20201211185032.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030533786 $9 978-3-030-53378-6
024 7 $a 10.1007/978-3-030-53378-6 $2 doi
035 $a 978-3-030-53378-6
050 4 $a QA251.5
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
072 7 $a PBF $2 thema
082 0 4 $a 512.46 $2 23
100 1 $a Fajardo, William. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327739
245 1 0 $a Skew PBW Extensions $h [electronic resource] : $b Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications / $c by William Fajardo, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, Helbert Venegas.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XV, 584 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Algebra and Applications, $x 1572-5553 ; $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 Gröbner 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 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.
650 2 4 $a Category Theory, Homological Algebra. $3 678397
650 1 4 $a Associative Rings and Algebras. $3 672306
650 0 $a Algorithms. $3 527865
650 0 $a Homological algebra. $3 1255326
650 0 $a Category theory (Mathematics). $3 1255325
650 0 $a Rings (Algebra). $3 685051
650 0 $a Associative rings. $3 893564
700 1 $a Venegas, Helbert. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327744
700 1 $a Suárez, Héctor. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327743
700 1 $a Reyes, Armando. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327742
700 1 $a Lezama, Oswaldo. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327741
700 1 $a Gallego, Claudia. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1327740
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030533779
776 0 8 $i Printed edition: $z 9783030533793
776 0 8 $i Printed edition: $z 9783030533809
830 0 $a Algebra and Applications, $x 1572-5553 ; $v 20 $3 1261460
856 4 0 $u https://doi.org/10.1007/978-3-030-53378-6
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)