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Skew PBW Extensions - Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications (Paperback, 1st ed. 2020)
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Skew PBW Extensions - Ring and Module-theoretic Properties, Matrix and Groebner Methods, and Applications (Paperback, 1st ed. 2020)
Series: Algebra and Applications, 28
Expected to ship within 10 - 15 working days
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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.
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