Strongly compressible modules and semiprime right goldie rings |
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Authors: | Yiqiang Zhou |
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Institution: | Mathematics Department , The University of British Columbia , V6T 122, Vancouver, Canada |
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Abstract: | A module M R is defined to be strongly compressible (or SC for short) if for every essential submodule N of M, there exists X ? E(M) such that M ? X ? N. We show that a ring R is semiprime right Goldie iff R Ris SC module iff every right ideal of R is SC module iff every submodule of each progenerator of Mod-R is SC module. As corollaries of this result, we obtain some new module-theoretic characterizations of semiprime Goldie rings, prime (right) Goldie rings and Prüfer rings, etc., etc.,respectively. And the characterization theorem of semiprime Goldie rings of López-Permouth, Rizvi and Yousif by using weakly-injective modules can be regarded as a corollary of our results. |
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