Gröbner bases in ring theory /:
This monograph strives to introduce a solid foundation on the usage of Grobner 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 Grobner bases, presents a constructive PBW theory in a qu...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New Jersey :
World Scientific,
©2012.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This monograph strives to introduce a solid foundation on the usage of Grobner 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 Grobner 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 Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi- )primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non- )homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations). |
| Beschreibung: | 1 online resource (x, 284 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 271-280) and index. |
| ISBN: | 9789814365147 9814365149 1299671837 9781299671836 |
Internformat
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| 504 | |a Includes bibliographical references (pages 271-280) and index. | ||
| 505 | 0 | |a Introduction -- Preliminaries -- The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- Gröbner bases: conception and construction -- Gröbner basis theory meets PBW theory -- Using A[beta][subscript LH] in terms of Gröbner bases -- Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- A study of Rees algebra by Gröbner bases -- Looking for more Gröbner bases. | |
| 588 | 0 | |a Print version record. | |
| 520 | |a This monograph strives to introduce a solid foundation on the usage of Grobner 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 Grobner 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 Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi- )primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non- )homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations). | ||
| 600 | 1 | 0 | |a Gröbner, Wolfgang, |d 1899-1980. |0 http://id.loc.gov/authorities/names/n84802844 |
| 600 | 1 | 7 | |a Gröbner, Wolfgang, |d 1899-1980 |2 fast |1 https://id.oclc.org/worldcat/entity/E39PBJtmxBBhBt7WxyD6JBPxXd |
| 650 | 0 | |a Gröbner bases. |0 http://id.loc.gov/authorities/subjects/sh92005856 | |
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| 758 | |i has work: |a Gröbner bases in ring theory (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFP7dyqH88YD7JpDmrpMRq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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| 880 | 0 | |6 505-00/(S |a Machine generated contents note: 1. Preliminaries -- 1.1. Presenting Algebras by Relations -- 1.2.S-Graded Algebras and Modules -- 1.3.T-Filtered Algebras and Modules -- 2. The Γ-Leading Homogeneous Algebra Ar/LH -- 2.1. Recognizing a via GΓ (A): Part 1 -- 2.2. Recognizing a via GΓ (A): Part 2 -- 2.3. The Γ-Graded Isomorphism Ar/LH Gr (A) -- 2.4. Recognizing a via Ar/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 K (X1 ..., Xn) and KQ -- 3.6.(De)homogenized Grobner Bases -- 3.7. Dh-Closed Homogeneous Grobner Bases -- 4. Grobner Basis Theory Meets PBW Theory -- 4.1.R -Standard Basis and R -Pbw Isomorphism -- 4.2. Realizing r -PBW Isomorphism by Grobner Basis -- 4.3. Classical PBW K -Bases vs Grobner Bases -- 4.4. Solvable Polynomial Algebras Revisited. | |
| 880 | 0 | |6 505-00/(S |a Contents note continued: 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 Algebras -- 5.7. Recognizing Finiteness of Global Dimension -- 5.8. Determination of Hilbert Series -- 6. Recognizing (Non- )Homogeneous p- Koszulity via AB/LH -- 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). | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn785127178 |
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| _version_ | 1816881791332515840 |
| adam_text | |
| any_adam_object | |
| author | Li, Huishi |
| author_GND | http://id.loc.gov/authorities/names/n96066476 |
| author_facet | Li, Huishi |
| author_role | |
| author_sort | Li, Huishi |
| author_variant | h l hl |
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| callnumber-label | QA251 |
| callnumber-raw | QA251.3 .L5 2012eb |
| callnumber-search | QA251.3 .L5 2012eb |
| callnumber-sort | QA 3251.3 L5 42012EB |
| callnumber-subject | QA - Mathematics |
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| collection | ZDB-4-EBA |
| contents | Introduction -- Preliminaries -- The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- Gröbner bases: conception and construction -- Gröbner basis theory meets PBW theory -- Using A[beta][subscript LH] in terms of Gröbner bases -- Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- A study of Rees algebra by Gröbner bases -- Looking for more Gröbner bases. |
| ctrlnum | (OCoLC)785127178 |
| dewey-full | 512.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.4 |
| dewey-search | 512.4 |
| dewey-sort | 3512.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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tag="505" ind1="0" ind2=" "><subfield code="a">Introduction -- Preliminaries -- The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- Gröbner bases: conception and construction -- Gröbner basis theory meets PBW theory -- Using A[beta][subscript LH] in terms of Gröbner bases -- Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- A study of Rees algebra by Gröbner bases -- Looking for more Gröbner bases.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. 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Preliminaries -- 1.1. Presenting Algebras by Relations -- 1.2.S-Graded Algebras and Modules -- 1.3.T-Filtered Algebras and Modules -- 2. The Γ-Leading Homogeneous Algebra Ar/LH -- 2.1. Recognizing a via GΓ (A): Part 1 -- 2.2. Recognizing a via GΓ (A): Part 2 -- 2.3. The Γ-Graded Isomorphism Ar/LH Gr (A) -- 2.4. Recognizing a via Ar/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 K (X1 ..., Xn) and KQ -- 3.6.(De)homogenized Grobner Bases -- 3.7. Dh-Closed Homogeneous Grobner Bases -- 4. Grobner Basis Theory Meets PBW Theory -- 4.1.R -Standard Basis and R -Pbw Isomorphism -- 4.2. Realizing r -PBW Isomorphism by Grobner Basis -- 4.3. Classical PBW K -Bases vs Grobner Bases -- 4.4. Solvable Polynomial Algebras Revisited.</subfield></datafield><datafield tag="880" ind1="0" ind2=" "><subfield code="6">505-00/(S</subfield><subfield code="a">Contents note continued: 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 Algebras -- 5.7. Recognizing Finiteness of Global Dimension -- 5.8. Determination of Hilbert Series -- 6. Recognizing (Non- )Homogeneous p- Koszulity via AB/LH -- 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. 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| id | ZDB-4-EBA-ocn785127178 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:20Z |
| institution | BVB |
| isbn | 9789814365147 9814365149 1299671837 9781299671836 |
| language | English |
| oclc_num | 785127178 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 284 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Li, Huishi. http://id.loc.gov/authorities/names/n96066476 Gröbner bases in ring theory / Huishi Li. New Jersey : World Scientific, ©2012. 1 online resource (x, 284 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 271-280) and index. Introduction -- Preliminaries -- The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- Gröbner bases: conception and construction -- Gröbner basis theory meets PBW theory -- Using A[beta][subscript LH] in terms of Gröbner bases -- Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- A study of Rees algebra by Gröbner bases -- Looking for more Gröbner bases. Print version record. This monograph strives to introduce a solid foundation on the usage of Grobner 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 Grobner 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 Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi- )primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non- )homogeneous p-Koszulity, PBW-deformation, and regular central extension. With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations). Gröbner, Wolfgang, 1899-1980. http://id.loc.gov/authorities/names/n84802844 Gröbner, Wolfgang, 1899-1980 fast https://id.oclc.org/worldcat/entity/E39PBJtmxBBhBt7WxyD6JBPxXd Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Bases de Gröbner. Anneaux (Algèbre) MATHEMATICS Algebra Intermediate. bisacsh Gröbner bases fast Rings (Algebra) fast Computeralgebra gnd http://d-nb.info/gnd/4010449-7 Gröbner-Basis gnd http://d-nb.info/gnd/4276378-2 Ringtheorie gnd http://d-nb.info/gnd/4126571-3 has work: Gröbner bases in ring theory (Text) https://id.oclc.org/worldcat/entity/E39PCFP7dyqH88YD7JpDmrpMRq https://id.oclc.org/worldcat/ontology/hasWork Print version: Li, Huishi. Gröbner bases in ring theory. Singapore ; Hackensack, NJ : World Scientific Publishing Co., ©2012 9789814365130 (OCoLC)730403765 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521267 Volltext 505-00/(S Machine generated contents note: 1. Preliminaries -- 1.1. Presenting Algebras by Relations -- 1.2.S-Graded Algebras and Modules -- 1.3.T-Filtered Algebras and Modules -- 2. The Γ-Leading Homogeneous Algebra Ar/LH -- 2.1. Recognizing a via GΓ (A): Part 1 -- 2.2. Recognizing a via GΓ (A): Part 2 -- 2.3. The Γ-Graded Isomorphism Ar/LH Gr (A) -- 2.4. Recognizing a via Ar/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 K (X1 ..., Xn) and KQ -- 3.6.(De)homogenized Grobner Bases -- 3.7. Dh-Closed Homogeneous Grobner Bases -- 4. Grobner Basis Theory Meets PBW Theory -- 4.1.R -Standard Basis and R -Pbw Isomorphism -- 4.2. Realizing r -PBW Isomorphism by Grobner Basis -- 4.3. Classical PBW K -Bases vs Grobner Bases -- 4.4. Solvable Polynomial Algebras Revisited. 505-00/(S Contents note continued: 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 Algebras -- 5.7. Recognizing Finiteness of Global Dimension -- 5.8. Determination of Hilbert Series -- 6. Recognizing (Non- )Homogeneous p- Koszulity via AB/LH -- 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). |
| spellingShingle | Li, Huishi Gröbner bases in ring theory / Introduction -- Preliminaries -- The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- Gröbner bases: conception and construction -- Gröbner basis theory meets PBW theory -- Using A[beta][subscript LH] in terms of Gröbner bases -- Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- A study of Rees algebra by Gröbner bases -- Looking for more Gröbner bases. Gröbner, Wolfgang, 1899-1980. http://id.loc.gov/authorities/names/n84802844 Gröbner, Wolfgang, 1899-1980 fast https://id.oclc.org/worldcat/entity/E39PBJtmxBBhBt7WxyD6JBPxXd Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Bases de Gröbner. Anneaux (Algèbre) MATHEMATICS Algebra Intermediate. bisacsh Gröbner bases fast Rings (Algebra) fast Computeralgebra gnd http://d-nb.info/gnd/4010449-7 Gröbner-Basis gnd http://d-nb.info/gnd/4276378-2 Ringtheorie gnd http://d-nb.info/gnd/4126571-3 |
| subject_GND | http://id.loc.gov/authorities/names/n84802844 http://id.loc.gov/authorities/subjects/sh92005856 http://id.loc.gov/authorities/subjects/sh85114140 http://d-nb.info/gnd/4010449-7 http://d-nb.info/gnd/4276378-2 http://d-nb.info/gnd/4126571-3 |
| 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 | Gröbner, Wolfgang, 1899-1980. http://id.loc.gov/authorities/names/n84802844 Gröbner, Wolfgang, 1899-1980 fast https://id.oclc.org/worldcat/entity/E39PBJtmxBBhBt7WxyD6JBPxXd Gröbner bases. http://id.loc.gov/authorities/subjects/sh92005856 Rings (Algebra) http://id.loc.gov/authorities/subjects/sh85114140 Bases de Gröbner. Anneaux (Algèbre) MATHEMATICS Algebra Intermediate. bisacsh Gröbner bases fast Rings (Algebra) fast Computeralgebra gnd http://d-nb.info/gnd/4010449-7 Gröbner-Basis gnd http://d-nb.info/gnd/4276378-2 Ringtheorie gnd http://d-nb.info/gnd/4126571-3 |
| topic_facet | Gröbner, Wolfgang, 1899-1980. Gröbner, Wolfgang, 1899-1980 Gröbner bases. Rings (Algebra) Bases de Gröbner. Anneaux (Algèbre) MATHEMATICS Algebra Intermediate. Gröbner bases Computeralgebra Gröbner-Basis Ringtheorie |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521267 |
| work_keys_str_mv | AT lihuishi grobnerbasesinringtheory |