GROBNER BASES IN RING THEORY

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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.