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Paper   IPM / M / 7376
School of Mathematics
  Title:   On λ-finitely embedded modules
  Author(s):  O. A. S. Karamzadeh (Joint with Sh. Rahimpour)
  Status:   Published
  Journal: Algebra Colloq.
  Vol.:  12
  Year:  2005
  Pages:   281-292
  Supported by:  IPM
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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