Cyclic modules and the structure of rings
 Author/Creator
 Jain, S. K.
 Language
 English.
 Edition
 1st ed.
 Imprint
 Oxford, U.K. : Oxford University Press, 2012.
 Physical description
 x, 220 p. ; 24 cm.
 Series
 Oxford mathematical monographs.
Access
Contributors
 Contributor
 Srivastava, Ashish.
 Tuganbaev, Askar A.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [207]218) and index.
 Contents

 Preface  1. Preliminaries  2. Rings characterized by their proper factor rings  3. Rings each of whose proper cyclic modules has a chain condition  4. Rings each of whose cyclic modules is injective (or CS)  5. Rings each of whose proper cyclic modules is injective  6. Rings each of whose simple modules is injective (or injective)  7. Rings each of whose (proper) cyclic modules is quasiinjective  8. Rings each of whose (proper) cyclic modules is continuous  9. Rings each of whose (proper) cyclic modules is piinjective  10. Rings with cyclics @0injective, weakly injective or quasiprojective  11. Hypercyclic, qhypercyclic and pihypercyclic rings  12. Cyclic modules essentially embeddable in free modules  13. Serial and distributive modules  14. Rings characterized by decompositions of their cyclic modules  15. Rings each of whose modules is a direct sum of cyclic modules  16. Rings each of whose modules is an I0module  17. Completely integrally closed modules and rings  18. Rings each of whose cyclic modules is completely integrally closed  19. Rings characterized by their onesided ideals  References  Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 This unique and comprehensive volume provides an uptodate account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a oneyear graduate course in the theory of rings and modules.
(source: Nielsen Book Data)
Subjects
 Subject
 Noncommutative rings.
 Cycles.
Bibliographic information
 Publication date
 2012
 Responsibility
 S.K. Jain, Ashish K. Srivastava, Askar A. Tuganbaev.
 Series
 Oxford mathematical monographs
 ISBN
 9780199664511
 019966451X