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Paper   IPM / M / 7399
School of Mathematics
  Title:   Endoprime modules
1.  A. Haghany
2.  M. R. Vedadi
  Status:   Published
  Journal: Acta Math. Hungar.
  Vol.:  106
  Year:  2005
  Pages:   89-99
  Supported by:  IPM
An endoprime R-module M is a nonzero module whose nonzero fully invariant submodules are faithful over END(MR). Such modules have prime endomorphism rings. The class of endoprime modules properly contains the class of prime modules in the sense of Zelmanowitz [5], and the class of prime modules with condition (∗) of Wisbauer [4]. While over commutative rings, endoprime modules are prime, in general, prime and endoprime are different conditions. A nonzero right R-Module M is a direct sum of isomorphic simple modules if and only if each nonzero element of σ[M] is an endoprime module. Various properties of endoprime modules including their Morita invariance, are obtained, and the structure of endomprphism rings of certain endoprime modules are determined.

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