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  • 1 University of Transkei Private Bag X1 Untata Transkei South Africa Private Bag X1 Untata Transkei South Africa
  • 2 University of Port Elizabeth P. O. Box. 1600 6000 Port Elizabeth South Africa P. O. Box. 1600 6000 Port Elizabeth South Africa
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Abstract  

We define a prime ΓM-module for a Γ-ringM. It is shown that a subsetP ofM is a prime ideal ofM if and only ifP is the annihilator of some prime ΓM-moduleG. s-prime ideals ofM were defined by the first author. We defines-modules ofM, analogous to a concept defined by De Wet for rings. It is shown that a subsetQ ofM is ans-prime ideal ofM if and only ifQ is the annihilator of somes-moduleG ofM. Relationships between prime ΓM-modules and primeR-modules are established, whereR is the right operator ring ofM. Similar results are obtained fors-modules.