Noncommutative Polynomial Algebras of Solvable Type and Their Modules
Basic Constructive-Computational Theory and Methods
1st Edition
Published on 8. November 2021
Book
Hardback
218 pages
978-1-032-07988-2 (ISBN)
Description
Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the ?rst book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers:
A constructive introduction to solvable polynomial algebras and Groebner basis theory for left ideals of solvable polynomial algebras and submodules of free modules
The new ?ltered-graded techniques combined with the determination of the existence of graded monomial orderings
The elimination theory and methods (for left ideals and submodules of free modules) combining the Groebner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of di?erent kinds of elimination orderings
The computational construction of ?nite free resolutions (including computation of syzygies, construction of di?erent kinds of ?nite minimal free resolutions based on computation of di?erent kinds of minimal generating sets), etc.
This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.
A constructive introduction to solvable polynomial algebras and Groebner basis theory for left ideals of solvable polynomial algebras and submodules of free modules
The new ?ltered-graded techniques combined with the determination of the existence of graded monomial orderings
The elimination theory and methods (for left ideals and submodules of free modules) combining the Groebner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of di?erent kinds of elimination orderings
The computational construction of ?nite free resolutions (including computation of syzygies, construction of di?erent kinds of ?nite minimal free resolutions based on computation of di?erent kinds of minimal generating sets), etc.
This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 17 mm
Weight
517 gr
ISBN-13
978-1-032-07988-2 (9781032079882)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Huishi Li
Noncommutative Polynomial Algebras of Solvable Type and Their Modules
Basic Constructive-Computational Theory and Methods
E-Book
11/2021
1st Edition
Chapman & Hall/CRC
€225.99
Available for download
Huishi Li
Noncommutative Polynomial Algebras of Solvable Type and Their Modules
Basic Constructive-Computational Theory and Methods
E-Book
11/2021
1st Edition
Chapman & Hall/CRC
€225.99
Available for download
Person
Huishi Li is an emeritus Professor at the Hainan University (China). He received his PhD degree from the University of Antwerp (Belgium) under the supervision of Professor, Doctor Fred Van Oystaeyen in 1990. His research interests include noncommutative rings and algebras, ltered and graded rings, noncommutative Groebner basis theory and applications to noncommutative algebras. He has authored or co-authored six research books (five of them are written in English and one of them is written in Chinese). Before working at the Hainan University (China), he worked at the Shaanxi Normal Universty (China), the Bilkent University (Turkey), and the Jiaying University (China) respectively. He was also a visiting scholar at the Bielefeld University (Germany), the Antwerp University (Belgium), and the University of Reims (France) respectively. After retiring from the Hainan University, he worked at the Kashgar University (China) as a volunteer teacher of mathematics for one year, and he is now a volunteer teacher of mathematics at the Xinjiang Institute of Technology (China).
Content
1. Solvable Polynomial Algebras. 1.1. Definition, Examples, Basic Properties. 1.2. A Constructive Characterization. 1.3. The Solvable Polynomial Algebras H(A). 1.4. Groebner Bases of Left Ideals. 1.5. Finite Groebner Bases ? The Noetherianess. 1.6. Elimination in Left Ideals. 2. Groebner Basis Theory of Free Modules. 2.1. Monomial Orderings on Free Modules. 2.2. Groebner Bases of Submodules. 2.3. The Noncommutative Buchberger Algorithm. 2.4. Elimination in Submodules. 2.5. Application to Module Homomorphisms. 3. Computation of Finite Free Resolutions and Projective Dimension. 3.1. Computation of Syzygies. 3.2. Computation of Finite Free Resolutions. 3.3. Global Dimension and Stability. 3.4. Computation of p.dimAM. 4. Computation of Minimal Finite Graded Free Resolutions. 4.1. N-graded Solvable Polynomial Algebras of (B; d( ))-type. 4.2. N-Graded Free Modules. 4.3. Computation of Minimal Homogeneous Generating Sets. 5. Computation of Minimal Finite Filtered Free Resolutions. 5.1. N-Filtered Solvable Polynomial Algebras of (B; d( ))-Type. 5.2. N-Filtered Free Modules. 5.3. Filtered-Graded Transfer of Groebner Bases for Modules. 5.4. F-Bases and Standard Bases with Respect to Good Filtration. 5.5. Computation of Minimal F-Bases and Minimal Standard Bases. 5.6. Minimal Filtered Free Resolutions and Their Uniqueness. 5.7. Computation of Minimal Finite Filtered Free Resolutions. Appendix.