Journal Name:
- European Journal of Pure and Applied Mathematics
| Author Name | University of Author |
|---|---|
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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