Abstract:
Let PP be a topological module (over the ring of polynomials) of vector-valued functions f:G→Cqf:G→Cq, holomorphic in a domain G⊂CG⊂C.
A closed submodule I⊂PI⊂P is local (that is, uniquely determined by the collection IλIλ, λ∈Gλ∈G, of its localized submodules) if and only if II is stable and saturated. A submodule is said to be stable if it admits division by binomials: f∈If∈I, fz−λ∈Iλ⇒fz−λ∈Ifz−λ∈Iλ⇒fz−λ∈I.
Being saturated amounts to possessing sufficiently many elements.
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Citation:
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