LEADER 02781oam 2200505 450 001 996418188403316 005 20210602224143.0 010 $a3-030-53378-6 024 7 $a10.1007/978-3-030-53378-6 035 $a(CKB)4100000011645311 035 $a(DE-He213)978-3-030-53378-6 035 $a(MiAaPQ)EBC6424410 035 $a(PPN)252515382 035 $a(EXLCZ)994100000011645311 100 $a20210602d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSkew pbw extensions $ering and module-theoretic properties, matrix and gröbner methods, and applications /$fWilliam Fajardo, 5 others 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XV, 584 p.) 225 1 $aAlgebra and Applications,$x1572-5553 ;$v28 311 $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,$x1572-5553 ;$v28 606 $aRing extensions (Algebra) 606 $aNoncommutative rings 606 $aCategories (Mathematics) 615 0$aRing extensions (Algebra) 615 0$aNoncommutative rings. 615 0$aCategories (Mathematics) 676 $a700 700 $aFajardo$b William$0981433 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418188403316 996 $aSkew pbw extensions$92240089 997 $aUNISA