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Skew PBW Extensions : Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications (1st ed. 2020)

By: Fajardo, William Gallego, Claudia Lezama, Oswaldo Reyes, Armando Suarez, Hector Venegas, Helbert

Part of the Algebra and Applications series
3030533778 / 9783030533779
Hardback
25/10/2020
Published 25/10/2020
Switzerland
155 x 235 mm Approx. 585 p.
Professional & Vocational  Learn More

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.

BIC:

PBC Mathematical foundations, PBF Algebra, PBKS Numerical analysis

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