The present book contains a complete and rigorous treatment of
Grobner bases for modules over commutative polynomial rings with
coefficients in Noetherian rings (with some other natural
computational conditions), and shows also non-trivial applications
of this theory in homological algebra. Algorithmic proofs of some
classical theorems of homological algebra using Grobner 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 Grobner and also presents constructive proofs of three
key theorems: Hilbert's Syzygy Theorem, Serre's Theorem, and
Quillen-Suslin 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.
General
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