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“School of Mathematics”

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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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