Abstract:
Let R ⊆ S be a ring extension, and let A be an
R-submodule of S. The saturation of A (in S) by τ is set A[τ] =
{x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset
of R. We study properties of saturations of R-submodules of S. We
use this notion of saturation to characterize star operations ⋆ on
ring extensions R ⊆ S satisfying the relation (A ∩ B)
⋆ = A⋆ ∩ B⋆
whenever A and B are two R-submodules of S such that AS =
BS = S.
