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| Paper IPM / M / 7376 |
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| Abstract: | |
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In this article, we introduce and study the notion of
λ-finitely embedded modules (a 0-finitely embedded module
is just a finitely embedded module). We extend some of the basic
results of f.e. modules to λ-f.e. modules. We use this
concept to give a new proof of a known result which essentially
says that a module M has Krull dimension α if and only if
each factor module M is λ-f.e. for some λ ≤ α and α is the least ordinal with this
property. It is observed that a semiprime ring R has Krull
dimension λ if and only if R is λ-f.e. We
improve the theorem of Matlis-Papp and some of its consequences.
Finally, some known results in the literature are restated in
terms of the above notion.
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