Edition:

2

Publisher:

University of Chicago Press

Number of Pages:

207

Price:

27.00

ISBN:

0-226-42451-0

Date Received:

Tuesday, February 1, 2005

Reviewable:

Yes

Series:

Chicago Lectures in Mathematics Series

Publication Date:

1995

Format:

Paperback

Audience:

Category:

Monograph

BLL Committee

02/12/2009

Preface

Pt. I: Fields

1: Field extensions

2: Ruler and compass constructions

3: Foundations of Galois theory

4: Normality and stability

5: Splitting fields

6: Radical extensions

7: The trace and norm theorems

8: Finite fields

9: Simple extensions

10: Cubic and quartic equations

11: Separability

12: Miscellaneous results on radical extensions

13: Infinite algebraic extensions

Pt. II: Rings

1: The radical

2: Primitive rings and the density theorem

3: Semi-simple rings

4: The Wedderburn principal theorem

5: Theorems of Hopkins and Levitzki

6: Primitive rings with minimal ideals and dual vector spaces

7: Simple rings

Pt. III: Homological Dimension

1: Dimension of modules

2: Global dimension

3: First theorem on change of rings

4: Polynomial rings

5: Second theorem on change of rings

6: Third theorem on change of rings

7: Localization

8: Preliminary lemmas

9: A regular ring has finite global dimension

10: A local ring of finite global dimension is regular

11: Injective modules

12: The group of homomorphisms

13: The vanishing of Ext

14: Injective dimension

Notes

Index

Pt. I: Fields

1: Field extensions

2: Ruler and compass constructions

3: Foundations of Galois theory

4: Normality and stability

5: Splitting fields

6: Radical extensions

7: The trace and norm theorems

8: Finite fields

9: Simple extensions

10: Cubic and quartic equations

11: Separability

12: Miscellaneous results on radical extensions

13: Infinite algebraic extensions

Pt. II: Rings

1: The radical

2: Primitive rings and the density theorem

3: Semi-simple rings

4: The Wedderburn principal theorem

5: Theorems of Hopkins and Levitzki

6: Primitive rings with minimal ideals and dual vector spaces

7: Simple rings

Pt. III: Homological Dimension

1: Dimension of modules

2: Global dimension

3: First theorem on change of rings

4: Polynomial rings

5: Second theorem on change of rings

6: Third theorem on change of rings

7: Localization

8: Preliminary lemmas

9: A regular ring has finite global dimension

10: A local ring of finite global dimension is regular

11: Injective modules

12: The group of homomorphisms

13: The vanishing of Ext

14: Injective dimension

Notes

Index

Publish Book:

Modify Date:

Thursday, February 12, 2009

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