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Paper   IPM / M / 587
School of Mathematics
  Title:   A note on the countable union of prime submodules
1.  M. R. Pournaki
2.  M. Tousi
  Status:   Published
  Journal: Int. J. Math. Math. Sci.
  No.:  10
  Vol.:  27
  Year:  2001
  Pages:   641-643
  Publisher(s):   Hindawi
  Supported by:  IPM
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 bJ(R), M is complete with respect to the b-adic topology, {Pi}i ≥ 1 is a countable family of prime submodules of M, and xM, then x+N ⊆ ∪i ≥ 1 Pi implies that x+NPj for some j ≥ 1. This extends a theorem of Sharp and Vámos concerning prime ideals to prime submodules.

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