03570nam 22006495 450 99646661840331620200704164246.03-540-45765-810.1007/b84211(CKB)1000000000233285(SSID)ssj0000325197(PQKBManifestationID)11254093(PQKBTitleCode)TC0000325197(PQKBWorkID)10320530(PQKB)11054626(DE-He213)978-3-540-45765-7(MiAaPQ)EBC6303068(MiAaPQ)EBC5591446(Au-PeEL)EBL5591446(OCoLC)1066192407(PPN)155214691(EXLCZ)99100000000023328520121227d2002 u| 0engurnn|008mamaatxtccrNoncommutative Gröbner Bases and Filtered-Graded Transfer[electronic resource] /by Huishi Li1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (IX, 202 p.) Lecture Notes in Mathematics,0075-8434 ;1795Bibliographic Level Mode of Issuance: Monograph3-540-44196-4 Introduction -- Chapter I: Basic Structural Tricks and Examples -- Chapter II: Gröbner Bases in Associative Algebras -- Chapter III: Gröbner Bases and Basic Algebraic-Algorithmic Structures -- Chapter IV: Filtered-Graded Transfer of Gröbner Bases -- Chapter V: GK-dimension of Modules over Quadric Solvable Polynomial Algebras and Elimination of Variables -- Chapter VI: Multiplicity Computation of Modules over Quadric Solvable Polynomial Algebras -- Chapter VII: (partial-)Holonomic Modules and Functions over Quadric Solvable Polynomial Algebras -- Chapter VII: Regularity and Ko-group of Quadric Solvable Polynomial Algebras -- References -- Index.This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.Lecture Notes in Mathematics,0075-8434 ;1795Associative ringsRings (Algebra)AlgorithmsAssociative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Associative rings.Rings (Algebra).Algorithms.Associative Rings and Algebras.Algorithms.512.4Li Huishiauthttp://id.loc.gov/vocabulary/relators/aut56176MiAaPQMiAaPQMiAaPQBOOK996466618403316Noncommutative Gröbner bases and filtered-graded transfer262265UNISA