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 Gr bner 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. | Grobner Bases in Ring Theory by Huishi Li, Hardcover | Indigo Chapters