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On a Proper Subclass of Primeful Modules Which Contains the Class of Finitely Generated Modules Properly

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Abstract (2. Language): 
Let R be a commutative ring with identity and M a unital R-module. Moreover, let PSpec(M) denote the primary-like spectrum of M and Spec(R/Ann(M)) the prime spectrum of R/Ann(M). We define an R-module M to be a -module, if  : PSpec(M)→Spec(R/Ann(M)) given by (Q) =p(Q : M)/Ann(M) is a surjective map. The class of -modules is a proper subclass of primeful modules, called -modules here, and contains the class of finitely generated modules properly. Indeed,  and are two sides of a commutative triangle of maps between spectrums. We show that if R is an Artinian ring, then all R-modules are -modules and the converse is true when R is a Noetherian ring.
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REFERENCES

References: 

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