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Paper   IPM / M / 7729
School of Mathematics
  Title:   A new characterization of commutative Artinian rings
1.  K. Divaani-Aazar
2.  A. Mafi
  Status:   Published
  Journal: Vietnam J. Math.
  Vol.:  32
  Year:  2004
  Pages:   319-322
  Supported by:  IPM
Let R be a commutative Noetherian ring. It is shown that R is Artinian if and only if every R-module is good, if and only if every R-module is representable. As a result, it follows that every nonzero submodule of any representable R-module is representable if and only if R is Artinian. This provides an answer to a question which is investigated in [1].

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