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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.37 no.2 Antofagasta June 2018 


Saturations of submodules with respect to subsets of a ring

Javad Bagheri Harehdashti1 

Hosein Fazaeli Moghimi2 

1 University of Birjand, Department of Mathematics, Iran. E-mail:

2 University of Birjand, Department of Mathematics, Iran. E-mail:


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 (N)={m ∈ M : rm∈ N for some r∈ R\T}. In this article we study conditions under which (N) is a submodule of M and investigate when it is a union of prime submodules.

Keywords : Saturation; Prime submodule.

Subjclass : 13C99 (MSC date is wrong: these are MSC 2010). Primary: 91A46,

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[1] I. Kaplansky, Commutative Rings. The University of Chicago Press, (1974). [ Links ]

[2] C. P. Lu, Saturations of submodules, Comm. Algebra 31(6), pp. 2655-2673, (2003). [ Links ]

[3] C. P. Lu, A module whose prime spectrum has the surjective natural map, Houston J. Math. 33 (1), pp. 125-143, (2007). [ Links ]

Received: February 2017; Accepted: March 2018

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License