Cyclic Modules and the Structure of Rings

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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.

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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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Cyclic Modules and the Structure of Rings（Oxford Mathematical Monographs） 循环模与环结构 代数几何学

Cyclic Modules and the Structure of Rings（Oxford Mathematical Monographs）

循环模与环结构
代数几何学