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Rings characterized by their right ideals or cyclic modules
Published online by Cambridge University Press: 20 January 2009
It is well known that a ring R is semiprime Artinian if and only if every right ideal is an injective right R-module. In this paper we shall be concerned with the following general question: given a ring R all of whose right ideals have a certain property, what implications does this have for the ring R itself? In practice, it is not necessary to insist that all right ideals have the property, usually the maximal or essential right ideals will suffice. On the other hand, Osofsky proved that a ring R is semiprime Artinian if and only if every cyclic right R-module is injective. This leads to the second general question: given a ring R all of whose cyclic right R-modules have a certain property, what can one say about R itself?
- Research Article
- Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 3 , October 1989 , pp. 355 - 362
- Copyright © Edinburgh Mathematical Society 1989