Modules over endomorphism rings / Theodore G. Faticoni.

Format:

Book

Author/Creator:

Faticoni, Theodore G. (Theodore Gerard), 1954- author.

Series:

Encyclopedia of mathematics and its applications ; v. 130.

Encyclopedia of mathematics and its applications ; volume 130

Language:

English

Subjects (All):

Endomorphism rings.

Modules (Algebra).

Physical Description:

1 online resource (xx, 372 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

This is an extensive synthesis of recent work in the study of endomorphism rings and their modules, bringing together direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization. The main idea behind the book is to study modules G over a ring R via their endomorphism ring EndR(G). The author discusses a wealth of results that classify G and EndR(G) via numerous properties, and in particular results from point set topology are used to provide a complete characterization of the direct sum decomposition properties of G. For graduate students this is a useful introduction, while the more experienced mathematician will discover that the book contains results that are not otherwise available. Each chapter contains a list of exercises and problems for future research, which provide a springboard for students entering modern professional mathematics.

Contents:

1. Preliminary results

2. Class number of an abelian group

3. Mayer-Victoris sequences

4. Lifting units

5. conductor

6. Conductors and groups

7. Invertible fractional ideals

8. L-groups

9. Modules and homotopy classes

10. Tensor functor equivalences

11. Characterizing endomorphisms

12. Projective modules

13. Finitely generated modules

14. Rtffr E-projective groups

15. Injective endomorphism modules

16. diagram of categories

17. Diagrams of abelian groups

18. Marginal isomorphisms.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88585-5

1-107-10189-1

1-107-09938-2

1-107-09004-0

1-107-09320-1

1-107-08698-1

1-139-08734-7