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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 2943
   School of Mathematics
  Title: Associated prime submodules of finitely generated modules
  Author(s):
1 . K. Divaani-Aazar
2 . M.A. Esmkhani
  Status: Published
  Journal: Comm. Algebra
  Vol.: 33
  Year: 2005
  Pages: 4259 - 4266
  Supported by: IPM
  Abstract:
Let R be a commutative ring with identity. For a finitely generated R-module M, the notion of associated prime submodules of M is defined. It is shown that this notion inherits most of essential properties of the usual notion of associated prime ideals. In particular, it is proved that for a Noetherian multiplication module M, the set of associated prime submodules of M coincides with the set of M-radicals of primary submodules of M which appear in a minimal primary decomposition of the zero submodule of M. Also, Anderson's theorem [2] is extended to minimal prime submodules in a certain type of modules.

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