Abstract
ABSTRACT Let D be an integral domain with quotient field K and ⋆ a star-operation on D. Then ⋆ distributes over (finite) intersections if ∩ = (∩A α)⋆ for any (finite) collection {A α} of nonzero fractional ideals of D with ∩A α ≠ 0. This paper investigates star-operations that distribute over (finite) intersections. We also study the function defined on the set of nonzero fractional ideals of D given by A → A 𝒮 = {x ∈ K | xI ⊆ A for some I ∈ 𝒮} where 𝒮 is a multiplicatively closed set of ideals of D.
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