Huishi Li Knihy

Focusing on constructive-computational theory, this book presents foundational methods for exploring solvable polynomial algebras and their modules. It serves as a comprehensive introduction, making it ideal for researchers and postgraduate students in the field of noncommutative computational algebra. The systematic approach ensures that readers gain a solid understanding of the key concepts and techniques necessary for further investigation in this area.

Focusing on noncommutative associative algebras, this monograph presents a comprehensive introduction to Gr bner bases in ring theory. It explores their structural properties and offers a constructive PBW theory, revealing innovative methods to assess various algebraic characteristics such as Gelfand-Kirillov dimension and Noetherianity. The book includes numerous examples to clarify concepts and encourages further exploration of the topics. It is particularly valuable for researchers and graduate students in computational algebra and algebraic geometry, especially those interested in ring and module structure theory.

This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e. g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of ( q -)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.