Modules over Endomorphism Rings by Theodore G. Faticoni (English) Hardcover Book

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Modules over Endomorphism Rings by Theodore G. Faticoni

An extensive synthesis of recent work in the study of endomorphism rings and their modules, this book considers direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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.

Table of Contents

Preface; 1. Preliminary results; 2. Class number of an Abelian group; 3. Mayer-Vietoris sequences; 4. Lifting units; 5. The 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. A diagram of categories; 17. Diagrams of Abelian groups; 18. Marginal isomorphisms; References; Index.

Review

'Theodore Faticoni enriches the mathematical literature with a comprehensive and up-to-date account of the study of a large class of abelian groups presenting all the relevant results in a very well organised fashion … the book is a succession of very sharp results, which are the fruits of methodical and thorough investigations started about 40 years ago by the author. Page after page, Faticoni engages the reader in a friendly mathematical discussion. As incentive, he provides some historical motivations for the questions he considers, for example, the classification of algebraic number fields, which goes back to Gauss and Kummer, while numerous examples, exercises and problems for future research at the end of each chapter will certainly provide the reader with some stimulating challenges.' Bulletin of the London Mathematical Society

Promotional

An extensive synthesis of recent work in the study of endomorphism rings and their modules.

Review Quote

"This monograph is an up-to-date account of the intermingling of the theory of rtffr groups, ring theory, module theory, and number theory. Any researcher working in any of these areas should have a copy of this book." Manfred Dugas, Mathematical Reviews

Promotional \"Headline\"

An extensive synthesis of recent work in the study of endomorphism rings and their modules.

Description for Bookstore

An extensive synthesis of recent work in the study of endomorphism rings and their modules, this book considers direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.

Description for Library

An extensive synthesis of recent work in the study of endomorphism rings and their modules, this book considers direct sum decompositions of modules, the class number of an algebraic number field, point set topological spaces, and classical noncommutative localization.

Details ISBN0521199603 Author Theodore G. Faticoni Short Title MODULES OVER ENDOMORPHISM RING Publisher Cambridge University Press Language English ISBN-10 0521199603 ISBN-13 9780521199605 Media Book Format Hardcover Series Number 130 Year 2009 Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom DEWEY 512.4 Birth 1954 Affiliation Fordham University, Dept. of Mathematics, Bronx, NY Illustrations Worked examples or Exercises AU Release Date 2009-10-22 NZ Release Date 2009-10-22 UK Release Date 2009-10-22 Pages 392 Series Encyclopedia of Mathematics and its Applications Publication Date 2009-10-22 Alternative 9781139087346 Audience Professional & Vocational Product Class Description Mathematics Country of Origin US
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