Gröbner Bases in Commutative Algebra (Graduate Studies in Mathematics) 〈Vol. 130〉

Ene, Viviana

American Mathematical Society（2012/01発売）

• ページ数 173 p.
• 商品コード 9780821872871

基本説明

Provides a concise yet comprehensive and self-contained introduction. It especially aims to help young researchers become acquainted with fundamental tools and techniques related to Gröbner bases which are used in commutative algebra and to arouse their interest in exploring further topics such as toric rings, Koszul and Rees algebras, determinantal ideal theory, binomial edge ideals, and their applications to statistics.

Full Description

This book provides a concise yet comprehensive and self-contained introduction to Grobner basis theory and its applications to various current research topics in commutative algebra. It especially aims to help young researchers become acquainted with fundamental tools and techniques related to Grobner bases which are used in commutative algebra and to arouse their interest in exploring further topics such as toric rings, Koszul and Rees algebras, determinantal ideal theory, binomial edge ideals, and their applications to statistics. The book can be used for graduate courses and self-study. More than 100 problems will help the readers to better understand the main theoretical results and will inspire them to further investigate the topics studied in this book.

Contents

Polynomial rings and ideals
Grobner bases
First applications
Grobner bases for modules
Grobner bases of toric ideals
Selected applications in commutative algebra and combinatorics
Bibliography
Index