Matrix and Gröbner Methods in Homological Algebra: over Commutative Polynomial Rings - Softcover

Lezama Serrano, José Oswaldo

Softcover

ISBN 10: 3845430117 ISBN 13: 9783845430119

Publisher: LAP LAMBERT Academic Publishing, 2011

Synopsis

The present book contains a complete and rigorous treatment of Gröbner 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 Gröbner 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 Gröbner 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.

About this title

About the Author

PH.D. in Mathematics from the University of St. Petersburg, Full Professor at the Universidad Nacional de Colombia and awarded the Medal of Merit. Author of international publications in areas such as Rings and Modules, Groups of Matrices, Commutative Algebra, Algebraic Control Theory, Homological Algebra and Gröbner Bases.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2011
• Language: English
• ISBN 10: 3845430117
• ISBN 13: 9783845430119
• Binding: Paperback
• Number of pages: 192