The length of Artinian modules with countable Noetherian dimension
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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 $omega ^{alpha }+2leq it{l}(M)leq omega ^{alpha +1}$, 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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Journal title
volume 43 issue 6
pages 1621- 1628
publication date 2017-11-30
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