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| Paper IPM / M / 587 |
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| Abstract: | |||||
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Let M be a finitely-generated module over a Noetherian ring R.
Suppose a is an ideal of R and let N=a M and b=Ann(M/N). If b ⊆ J(R), M is complete with respect to the
b-adic topology, {Pi}i ≥ 1 is a countable family of
prime submodules of M, and x ∈ M, then x+N ⊆ ∪i ≥ 1 Pi implies that x+N ⊆ Pj for some j ≥ 1. This extends a theorem of Sharp and
Vámos concerning prime ideals to prime submodules.
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