Noncommutative Polynomial Algebras of Solvable Type and Their Modules: Basic Constructive-Computational Theory and Methods (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)

Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first 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 Gröbner basis theory for left ideals of solvable polynomial algebras and submodules of free modules
• The new filtered-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 Gröbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of different kinds of elimination orderings
• The computational construction of finite free resolutions (including computation of syzygies, construction of different kinds of finite minimal free resolutions based on computation of different 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.

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 Gröbner 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).