This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
This unique monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.
S. K. Jain is a Distinguished Professor Emeritus, Ohio University and Advisor, King Abdulaziz University. He was at the Department of Mathematics at Ohio University from 1970-2009. He is an Executive Editor of the Journal of Algebra and its Applications (World Scientific) and Bulletin of Mathematical Sciences (Springer). He is also on the editorial board of the Electronic Journal of Algebra. Ashish Srivastava is an Assistant Professor of Mathematics at Saint Louis University, Saint Louis, USA. He has written 15 research articles in Noncommutative Algebra and Combinatorics that have been published in various journals. Askar A. Tuganbaev is a Professor of Mathematics at the Russian State University of Trade and Economics, Moscow, Russia. He has written 10 monographs and more than 180 research articles in Algebra that have been published in various journals.
Inhaltsangabe
* 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 quasi-injective * 8: Rings each of whose (proper) cyclic modules is continuous * 9: Rings each of whose (proper) cyclic modules is pi-injective * 10: Rings with cyclics @0-injective, weakly injective or quasi-projective * 11: Hypercyclic, q-hypercyclic and pi-hypercyclic 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 I0-module * 17: Completely integrally closed modules and rings * 18: Rings each of whose cyclic modules is completely integrally closed * 19: Rings characterized by their one-sided ideals * References * Index
* 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 quasi-injective * 8: Rings each of whose (proper) cyclic modules is continuous * 9: Rings each of whose (proper) cyclic modules is pi-injective * 10: Rings with cyclics @0-injective, weakly injective or quasi-projective * 11: Hypercyclic, q-hypercyclic and pi-hypercyclic 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 I0-module * 17: Completely integrally closed modules and rings * 18: Rings each of whose cyclic modules is completely integrally closed * 19: Rings characterized by their one-sided ideals * References * Index
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