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Gröbner bases in ring theory /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Li, Huishi. | |
| 245 | 1 | 0 | |a Gröbner bases in ring theory / |c Huishi Li. |
| 260 | |a Singapore : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (x, 284 pages) | ||
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| 504 | |a Includes bibliographical references (pages 271-280) and index. | ||
| 505 | 0 | |6 880-01 |a Introduction -- 1. Preliminaries -- 2. The [gamma]-leading homogeneous algebra A[gamma][subscript LH] -- 3. Gröbner bases: conception and construction -- 4. Gröbner basis theory meets PBW theory -- 5. Using A[beta][subscript LH] in terms of Gröbner bases -- 6. Recognizing (non- )homogeneous [rho]-Koszul via A[beta][subscript LH] -- 7. A study of Rees algebra by Gröbner bases -- 8. Looking for more Gröbner bases. | |
| 520 | |a 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. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Gröbner bases. | |
| 650 | 0 | |a Rings (Algebra) | |
| 650 | 4 | |a Gr⁽obner bases. | |
| 650 | 6 | |a Bases de Gröbner. | |
| 650 | 6 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a Gröbner bases |2 fast | |
| 650 | 7 | |a Rings (Algebra) |2 fast | |
| 650 | 7 | |a Computeralgebra |2 gnd | |
| 650 | 7 | |a Gröbner-Basis |2 gnd | |
| 650 | 7 | |a Ringtheorie |2 gnd | |
| 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 | ||
| 776 | 0 | 8 | |i Print version: |a Li, Huishi. |t Gröbner bases in ring theory. |d Singapore : World Scientific, ©2012 |w (DLC) 2012359700 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=846136 |z Texto completo |
| 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 | |6 505-01/(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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