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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