Skew PBW Extensions

William Fajardo is a Professor of Mathematics at the Instituto Politécnico Grancolombiano, Bogotá, Colombia. His publications are in computational algebra. He received his Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogotá, Colombia in 2018.Claudia Gallego is a Professor of Mathematics at the Universidad Sergio Arboleda, Bogotá, Colombia. Her publications are in matrix and Gröbner methods in homological algebra and non-commutative algebra. She received her Ph.D. in mathematics from the Universidad Nacional de Colombia, Bogotá, 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, Bogotá, 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 Gröbner 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, Bogotá, 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, Bogotá, Colombia in 2013.Héctor Suárez is a Professor of Mathematics at the Universidad Pedagógica y Tecnológica 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, Bogotá, Colombia in 2017.Helbert Venegas is a Professor of Mathematics at the Universidad de la Sabana, Chía, 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, Bogotá, Colombia in 2020.

“The text under review attempts to summarize the breadth of research on skew PBW extensions since that initial paper. … Readers familiar with the area of skew PBW extensions may find this book a convenient reference.” (Jason Gaddis, Mathematical Reviews, June, 2023)“This very well-written book … . there are a few new techniques and approaches in the book via which the authors attack successfully the proofs of some classical results from this branch. Besides, certain innovations in the presentation of some specific moments in the subject are also demonstrated.” (Peter Danchev, zbMATH 1489.16002, 2022)

• 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.