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100   $a20201211d2020      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aSkew PBW Extensions $eRing and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications /$fby William Fajardo, Claudia Gallego, Oswaldo Lezama, Armando Reyes, Héctor Suárez, Helbert Venegas
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020.
215   $a1 online resource (XV, 584 p.) 
225 1 $aAlgebra and Applications,$x2192-2950 ;$v28
311 08$a3-030-53377-8 
327   $aPreface -- 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.
330   $aThis monograph is devoted to a new class of non-commutative rings, skew Poincaré?Birkhoff?Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gröbner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin?Schelter regular algebras, and the noncommutative Zariski cancellation problem. The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.
410  0$aAlgebra and Applications,$x2192-2950 ;$v28
606   $aAssociative rings
606   $aAssociative algebras
606   $aAlgebra, Homological
606   $aAlgorithms
606   $aAssociative Rings and Algebras
606   $aCategory Theory, Homological Algebra
606   $aAlgorithms
615  0$aAssociative rings.
615  0$aAssociative algebras.
615  0$aAlgebra, Homological.
615  0$aAlgorithms.
615 14$aAssociative Rings and Algebras.
615 24$aCategory Theory, Homological Algebra.
615 24$aAlgorithms.
676   $a700
700   $aFajardo$b William$0981433
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910484658703321
996   $aSkew pbw extensions$92240089
997   $aUNINA