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Matrix and Grbner Methods in Homological Algebra: over Commutative Polynomial Rings,Used
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The present book contains a complete and rigorous treatment of Grbner bases for modules over commutative polynomial rings with coefficients in Noetherian rings (with some other natural computational conditions), and shows also nontrivial applications of this theory in homological algebra. Algorithmic proofs of some classical theorems of homological algebra using Grbner bases and matrix constructive methods have been published in many recent papers, but there is not a book that contains both topics. In fact, probably there is not a monograph that simultaneously includes the theory of Grbner and also presents constructive proofs of three key theorems: Hilberts Syzygy Theorem, Serres Theorem, and QuillenSuslin Theorem. The main purpose of this book is to fill this lack. Some generalizations of these theorems to extended modules and rings from a constructive approach are also included.
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