The length of Artinian modules with countable Noetherian dimension

Document Type : Research Paper

Authors

Department of Mathematics‎, ‎Shahid Chamran University of Ahvaz‎, ‎Ahvaz‎, ‎Iran.

Abstract

‎It is shown that‎ ‎if $M$ is an Artinian module over a ring‎ ‎$R$‎, ‎then $M$ has Noetherian dimension $\alpha $‎, ‎where $\alpha $ is a countable ordinal number‎, ‎if and only if $\omega ^{\alpha }+2\leq \it{l}(M)\leq \omega ^{\alpha‎ +1}$, ‎where $ \it{l}(M)$ is‎ ‎the length of $M$‎, ‎$i.e.,$ the least ordinal number such that the interval $[0‎, ‎\ \it{l}(M))$ cannot be embedded in the lattice of all submodules of $M$.

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References

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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 6
November 2017
Pages 1621-1628

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History

  • Receive Date: 07 April 2016
  • Revise Date: 26 July 2016
  • Accept Date: 27 July 2016

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