Saturations of submodules with respect to subsets of a ring.
Keywords:
Saturation, Prime submoduleAbstract
Let R be a commutative ring with identity and M a unital R-module. For any submodule N of M and non-empty subset T of R, let SMT (N)={m ∈ M : rm∈ N for some r ∈ R\T}. In this article we study conditions under which SMT (N) is a submodule of M and investigate when it is a union of prime submodules.
References
I. Kaplansky, Commutative Rings.The University of Chicago Press, (1974).
C. P. Lu, Saturations of submodules, Comm. Algebra 31(6), pp. 2655-2673, (2003).
C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math. 33 (1), pp. 125-143, (2007).
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