Commutative algebra : an introduction / J. William Hoffman, Xiaohong Jia, Haohao Wang.

Format:

Book

Author/Creator:

Hoffman, Jerome William, 1952- author.

Jia, Xiaohong, author.

Wang, Haohao, author.

Language:

English

Subjects (All):

Commutative algebra.

Geometry, Algebraic.

Physical Description:

1 online resource (203 pages)

Edition:

1st ed.

Place of Publication:

Dulles, Virginia ; Boston, Massachusetts ; New Delhi, [India] : Mercury Learning & Information, 2016.

Contents:

Front Matter

Half Title

License Page

Title Page

Copyright Page

Contents

Preface

List of Figures

Body Matter

1. Introduction

2. Rings and Ideals

2.1 Rings and Ideals

2.2 Localization of a Ring

2.3 Ideals in a Polynomial Ring

2.4 Grobner Basis of an Ideal

2.5 Elimination and Extension

2.6 Implicitization

2.7 Schemes

2.8 Grobner Basis Applications

3. Modules

3.1 Modules

3.2 Exact Sequences and Commutative Diagrams

3.3 Projective and Injective Modules

3.4 Tensor Product of Modules

3.5 Flatness

3.6 Localization

3.7 Local Property

3.8 Associated Primes

3.9 Primary Decomposition of Modules

3.10 Modules of Finite Length

3.11 Krull Dimension of a Ring

3.12 Dimension of Modules

3.13 Rank of Modules

3.14 Computational Applications

4. Graded and Local Rings and Modules

4.1 Graded Rings and Modules

4.2 Graded Localization

4.3 Graded Associated Primes

4.4 Filtration

4.5 System of Parameters

4.6 Regular and Quasi-regular M-Sequence

4.7 Proj of a Graded Ring

4.8 Graded Free Resolution

4.9 Dimension and Multiplicity

4.10 Applications

5. Homological Method

5.1 Complexes

5.2 Complex of Tor

5.3 Koszul Complex

5.4 Regular Sequences

5.5 Regular Rings

5.6 Complex of Ext

5.7 Exactness Criteria for Complexes

5.8 Local Cohomology

5.9 Applications

Back Matter

BIbliography

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-944534-70-9