This monograph strives to introduce a solid foundation on the usage
of Groebner 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 Groebner 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 Groebner 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 Groebner
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).
General
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