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Torsion-Free Modules (Chicago Lectures in Mathematics)

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Torsion-Free Modules (Chicago Lectures in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

The subject of torsion-free modules over an arbitrary integral domain arises naturally as a generalization of torsion-free abelian groups. In this volume, Eben Matlis brings together his research on torsion-free modules that has appeared in a number of mathematical journals. Professor Matlis has reworked many of the proofs so that only an elementary knowledge of homological algebra and commutative ring theory is necessary for an understanding of the theory.

The first eight chapters of the book are a general introduction to the theory of torsion-free modules. This part of the book is suitable for a self-contained basic course on the subject. More specialized problems of finding all integrally closed D-rings are examined in the last seven chapters, where material covered in the first eight chapters is applied.

An integral domain is said to be a D-ring if every torsion-free module of finite rank decomposes into a direct sum of modules of rank 1. After much investigation, Professor Matlis found that an integrally closed domain is a D-ring if, and only if, it is the intersection of at most two maximal valuation rings.

Table of Contents

Introduction

1. Cotorsion modules

2. Completions

3. h-local rings

4. Reflexive rings

5. Noetherian reflexive rings

6. Torsionless rings

7. Completely reflexive rings

8. Maximal valuation rings

9. The two generator problem for ideals

10. Noetherian D-rings

11. Quasi-local D-rings

12. h-local D-rings

13. Rings of type I

14. Integrally closed D-rings

15. Hausdorff D-rings

Bibliography

Index

Product Details

ISBN:
9780226510743
Author:
Matlis, Eben
Publisher:
University of Chicago Press
Location:
Chicago
Subject:
Algebra - Linear
Subject:
Modules (algebra)
Subject:
Rings (algebra)
Subject:
Rings
Subject:
Modules
Subject:
Mathematics-Linear Algebra
Edition Description:
Paperback
Series:
Chicago Lectures in Mathematics (Paperback)
Series Volume:
no. 6
Publication Date:
19730131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
176
Dimensions:
7.97x5.24x.43 in. .30 lbs.

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Science and Mathematics » Mathematics » Algebra » Linear Algebra

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