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This monograph strives to introduce a solid foundation on the usage of Gröbner 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 Gröbner 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 Gröbner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand-Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finitenes

Gröbner bases. --- Rings (Algebra) --- Gröbner basis theory --- Commutative algebra --- Algebraic rings --- Ring theory --- Algebraic fields --- Gröbner, Wolfgang, --- Gröbner, W.