The Resource Gröbner bases in ring theory, Huishi Li, (electronic resource)

Gröbner bases in ring theory, Huishi Li, (electronic resource)

Label
Gröbner bases in ring theory
Title
Gröbner bases in ring theory
Statement of responsibility
Huishi Li
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
This monograph strives to introduce a solid foundation on the usage of Gröbner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Gröbner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Gröbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finitenes
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Li, Huishi
Dewey number
512.4
Index
index present
Language note
English
LC call number
QA251.3
LC item number
.L54 2012
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Gröbner bases
  • Rings (Algebra)
Label
Gröbner bases in ring theory, Huishi Li, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 271-280) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases
  • 3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property
  • 5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases
  • 8.1 Lifting (Finite) Grobner Bases from On(λji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (295 p.)
Form of item
online
Isbn
9789814365147
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000000087525
  • (EBL)846136
  • (SSID)ssj0000646028
  • (PQKBManifestationID)11940162
  • (PQKBTitleCode)TC0000646028
  • (PQKBWorkID)10685612
  • (PQKB)11361851
  • (MiAaPQ)EBC846136
  • (WSP)00008223
  • (EXLCZ)992550000000087525
Label
Gröbner bases in ring theory, Huishi Li, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 271-280) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Preface; Contents; 0. Introduction; 1. Preliminaries; 1.1 Presenting Algebras by Relations; 1.2 S-Graded Algebras and Modules; 1.3 -Filtered Algebras and Modules; 2. The -Leading Homogeneous Algebra A LH; 2.1 Recognizing A via G (A): Part 1; 2.2 Recognizing A via G (A): Part 2; 2.3 The -Graded Isomorphism A LH G (A); 2.4 Recognizing A via A LH; 3. Grobner Bases: Conception and Construction; 3.1 Monomial Ordering and Admissible System; 3.2 Division Algorithm and Grobner Basis; 3.3 Grobner Bases and Normal Elements; 3.4 Grobner Bases w.r.t. Skew Multiplicative K-Bases
  • 3.5 Grobner Bases in KhX1, . . . ,Xni and KQ3.6 (De)homogenized Grobner Bases; 3.7 dh-Closed Homogeneous Grobner Bases; 4. Grobner Basis Theory Meets PBW Theory; 4.1 -Standard Basis and -PBW Isomorphism; 4.2 Realizing - PBW Isomorphism by Grobner Basis; 4.3 Classical PBW K-Bases vs Grobner Bases; 4.4 Solvable Polynomial Algebras Revisited; 5. Using AB LH in Terms of Grobner Bases; 5.1 The Working Strategy; 5.2 Ufnarovski Graph; 5.3 Determination of Gelfand-Kirillov Dimension; 5.4 Recognizing Noetherianity; 5.5 Recognizing (Semi-)Primeness and PI-Property
  • 5.6 Anick's Resolution over Monomial Algebras5.7 Recognizing Finiteness of Global Dimension; 5.8 Determination of Hilbert Series; 6. Recognizing (Non-)Homogeneous p-Koszulity via ABLH; 6.1 (Non-)Homogeneous p-Koszul Algebras; 6.2 Anick's Resolution and Homogeneous p-Koszulity; 6.3 Working in Terms of Grobner Bases; 7. A Study of Rees Algebra by Grobner Bases; 7.1 Defining A by G*; 7.2 Defining A by G; 7.3 Recognizing Structural Properties of A via G; 7.4 An Application to Regular Central Extensions; 7.5 Algebras Defined by dh-Closed Homogeneous Grobner Bases; 8. Looking for More Grobner Bases
  • 8.1 Lifting (Finite) Grobner Bases from On(λji)8.2 Lifting (Finite) Grobner Bases from a Class of Algebras; 8.3 New Examples of Grobner Basis Theory; 8.4 Skew 2-Nomial Algebras; 8.5 Almost Skew 2-Nomial Algebras; Bibliography; Index
Dimensions
unknown
Extent
1 online resource (295 p.)
Form of item
online
Isbn
9789814365147
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2550000000087525
  • (EBL)846136
  • (SSID)ssj0000646028
  • (PQKBManifestationID)11940162
  • (PQKBTitleCode)TC0000646028
  • (PQKBWorkID)10685612
  • (PQKB)11361851
  • (MiAaPQ)EBC846136
  • (WSP)00008223
  • (EXLCZ)992550000000087525

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