A note on the countable union of prime submodules

M. R. Pournaki and M. Tousi

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-3

Abstract:

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, { P i } i ≥ 1 is a countable family of prime submodules of M , and x ∈ M , then x + N ⫅ ∪ i ≥ 1 P i implies that x + N ⫅ P j for some i ≥ 1 . This extends a theorem of Sharp and Vámos concerning prime ideals to prime submodules.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:313795

DOI: 10.1155/S0161171201011085

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