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Description of  An Introduction to Grobner Bases (Graduate Studies in Mathematics, Vol 3)

As the primary tool for doing explicit computations in polynomial rings in many variables, Grbner bases are an important component of all computer algebra systems. They are also important in computational commutative algebra and algebraic geometry. This book provides a leisurely and fairly comprehensive introduction to Grbner bases and their applications. Adams and Loustaunau cover the following topics: the theory and construction of Grbner bases for polynomials with coefficients in a field, applications of Grbner bases to computational problems involving rings of polynomials in many variables, a method for computing syzygy modules and Grbner bases in modules, and the theory of Grbner bases for polynomials with coefficients in rings. With over 120 worked out examples and 200 exercises, this book is aimed at advanced undergraduate and graduate students. It would be suitable as a supplement to a course in commutative algebra or as a textbook for a course in computer algebra or computational commutative algebra. This book would also be appropriate for students of computer science and engineering who have some acquaintance with modern algebra.