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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New Jersey :
World Scientific,
©2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000Ia 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn785127178 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
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| 008 | 120410s2012 njua ob 001 0 eng d | ||
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| 100 | 1 | |a Li, Huishi. | |
| 245 | 1 | 0 | |a Gröbner bases in ring theory / |c Huishi Li. |
| 260 | |a New Jersey : |b World Scientific, |c ©2012. | ||
| 300 | |a 1 online resource (x, 284 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 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). | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 600 | 1 | 0 | |a Gröbner, Wolfgang, |d 1899-1980. |
| 600 | 1 | 7 | |a Gröbner, Wolfgang, |d 1899-1980 |2 fast |
| 650 | 0 | |a Gröbner bases. | |
| 650 | 0 | |a Rings (Algebra) | |
| 650 | 6 | |a Bases de Gröbner. | |
| 650 | 6 | |a Anneaux (Algèbre) | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 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 | |
| 776 | 0 | 8 | |i Print version: |a Li, Huishi. |t Gröbner bases in ring theory. |d Singapore ; Hackensack, NJ : World Scientific Publishing Co., ©2012 |z 9789814365130 |w (OCoLC)730403765 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=521267 |z Texto completo |
| 880 | 0 | |6 505-00 |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 |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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