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Skew PBW Extensions

Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications
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Skew PBW Extensions by William Fajardo
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Description

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.

Author Biography

William Fajardo is a Professor of Mathematics at the Instituto Politecnico Grancolombiano, Bogota, Colombia. His publications are in computational algebra. He received his Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogota, Colombia in 2018. Claudia Gallego is a Professor of Mathematics at the Universidad Sergio Arboleda, Bogota, Colombia. Her publications are in matrix and Groebner methods in homological algebra and non-commutative algebra. She received her Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogota, Colombia in 2015, and was a postdoctoral researcher at the Universidad de Buenos Aires, Argentina. Oswaldo Lezama is the Director of the Seminar of Constructive Algebra-SAC2 at the Universidad Nacional de Colombia, Bogota, Colombia. The recipient of the 2017 National Mathematics Prize of the Columbian Mathematical Society, he is the author of five books and numerous research papers on rings and modules, matrix and Groebner methods in homological algebra, non-commutative algebra and non-commutative algebraic geometry. He has been an invited speaker at several international meetings. He received his Ph.D. in mathematics from Leningrad State University, Leningrad, USSR (today, St. Petersburg State University, St. Petersburg, Russia) in 1984. Armando Reyes is a Professor of Mathematics at the Universidad Nacional de Colombia, Bogota, Colombia. He is author of numerous research papers on rings and modules, non-commutative algebra and non-commutative algebraic geometry and has been an invited speaker at several international meetings. He received his Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogota, Colombia in 2013. Hector Suarez is a Professor of Mathematics at the Universidad Pedagogica y Tecnologica de Colombia, Tunja, Colombia. He is author of numerous research papers on rings and modules and non-commutative algebra. He received his Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogota, Colombia in 2017. Helbert Venegas is a Professor of Mathematics at the Universidad de la Sabana, Chia, Colombia. His publications are in non-commutative algebra and non-commutative algebraic geometry. He received his Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogota, Colombia in 2020.
Release date Australia
November 22nd, 2020
Country of Publication
Switzerland
Edition
1st ed. 2020
Illustrations
Approx. 585 p.
Imprint
Springer Nature Switzerland AG
Dimensions
165x220x25
ISBN-13
9783030533779
Product ID
33536814

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