Verfügbarkeit: Gröbner bases in ring theory

Gröbner bases in ring theory:

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Bibliographische Detailangaben
1. Verfasser:	Li, Huishi 1955- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Singapore [u.a.] World Scientific 2012
Schlagworte:	Ringtheorie Computeralgebra Gröbner-Basis
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	X, 284 S. graph. Darst.
ISBN:	9789814365130 9814365130

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MARC


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Datensatz im Suchindex

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adam_text	Contents Preface vii 0. Introduction 1 1. Preliminaries 7 1.1 Presenting Algebras by Relations .............. 7 1.2 S-Graded Algebras and Modules .............. 22 1.3 Г -Filtered Algebras and Modules .............. 26 2. The Г -Leadíng Homogeneous Algebra A^H 33 2.1 Recognizing A via Gr(A): Part 1.............. 33 2.2 Recognizing A via Gr(A): Part 2.............. 41 2.3 The r-Graded Isomorphism A[H -=-> Gr(A) ....... 50 2.4 Recognizing Л via А[н .................... 54 3. Gröbner Bases: Conception and Construction 57 3.1 Monomial Ordering and Admissible System ........ 58 3.2 Division Algorithm and Gröbner Basis ........... 63 3.3 Gröbner Bases and Normal Elements ............ 68 3.4 Gröbner Bases w.r.t. Skew Multiplicative if-Bases .... 71 3.5 Gröbner Bases in К(Хъ...,Хп) and KQ ......... 78 3-6 (De)homogenized Gröbner Bases .............. 96 3.7 dh-Closed Homogeneous Gröbner Bases .......... 112 4. Gröbner Basis Theory Meets PBW Theory 121 4.1 r-Standard Basis and Г -PBW Isomorphism ........ 122 χ Gröbner Bases in Ring Theory 4.2 Realizing Г -PBW Isomorphism by Gröbner Basis ..... 128 4.3 Classical PBW if-Bases vs Gröbner Bases ......... 133 4.4 Solvable Polynomial Algebras Revisited .......... 150 5. Using Aljj in Terms of Gröbner Bases 155 5.1 The Working Strategy .................... 155 5.2 Ufnarovski Graph ....................... 161 5.3 Determination of Gelfand-Kirillov Dimension ....... 165 5.4 Recognizing Noetherianity .................. 169 5.5 Recognizing (Semi-)Primeness and Pi-Property ...... 171 5.6 Anick s Resolution over Monomial Algebras ........ 177 5.7 Recognizing Finiteness of Global Dimension ........ 182 5.8 Determination of Hubert Series ............... 188 6. Recognizing (Non-)Homogeneous p-Koszulity via A®H 195 6.1 (Non-)Homogeneous p-Koszul Algebras ........... 196 6.2 Anick s Resolution and Homogeneous p-Koszulity ..... 197 6.3 Working in Terms of Gröbner Bases ............ 200 7. A Study of Rees Algebra by Gröbner Bases 205 7.1 Defining A by Q* ....................... 206 7.2 Defining A by Q ........... L ........... 208 7.3 Recognizing Structural Properties of A via Q ....... 211 7.4 An Application to Regular Central Extensions ...... 216 7.5 Algebras Defined by dh-Closed Homogeneous Gröbner Bases ............................. 219 8. Looking for More Gröbner Bases 223 8.1 Lifting (Finite) Gröbner Bases from On(Xjt) ........ 223 8.2 Lifting (Finite) Gröbner Bases from a Class of Algebras . 233 8.3 New Examples of Gröbner Basis Theory .......... 240 8.4 Skew 2-Nomial Algebras ................... 258 8.5 Almost Skew 2- Normal Algebras .............. 266 Bibliography 271 Index 281
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author	Li, Huishi 1955-
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discipline	Mathematik
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isbn	9789814365130 9814365130
language	English
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spelling	Li, Huishi 1955- Verfasser (DE-588)123969034 aut Gröbner bases in ring theory Huishi Li Singapore [u.a.] World Scientific 2012 X, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ringtheorie (DE-588)4126571-3 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Gröbner-Basis (DE-588)4276378-2 gnd rswk-swf Ringtheorie (DE-588)4126571-3 s Gröbner-Basis (DE-588)4276378-2 s Computeralgebra (DE-588)4010449-7 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022643183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Li, Huishi 1955- Gröbner bases in ring theory Ringtheorie (DE-588)4126571-3 gnd Computeralgebra (DE-588)4010449-7 gnd Gröbner-Basis (DE-588)4276378-2 gnd
subject_GND	(DE-588)4126571-3 (DE-588)4010449-7 (DE-588)4276378-2
title	Gröbner bases in ring theory
title_auth	Gröbner bases in ring theory
title_exact_search	Gröbner bases in ring theory
title_full	Gröbner bases in ring theory Huishi Li
title_fullStr	Gröbner bases in ring theory Huishi Li
title_full_unstemmed	Gröbner bases in ring theory Huishi Li
title_short	Gröbner bases in ring theory
title_sort	grobner bases in ring theory
topic	Ringtheorie (DE-588)4126571-3 gnd Computeralgebra (DE-588)4010449-7 gnd Gröbner-Basis (DE-588)4276378-2 gnd
topic_facet	Ringtheorie Computeralgebra Gröbner-Basis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022643183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT lihuishi grobnerbasesinringtheory

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