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“School of Mathematics”

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Paper   IPM / M / 7993
School of Mathematics
  Title:   Some criteria of cyclically pure injective modules
  Author(s): 
1.  K. Divaani-Azar
2.  M. A. Esmkhani
3.  M. Tousi
  Status:   Published
  Journal: J. Algebra
  Vol.:  304
  Year:  2006
  Pages:   367-381
  Supported by:  IPM
  Abstract:
The structure of cyclically pure injective modules over a commutative ring R is investigated and several characterization for them are presented. In particular, we prove that a module D is cyclically pure injective if and only if D is isomorphic to a direct summand of a module of the form Hom R(L, E) where L is the direct sum of a family of finitely presented cyclic modules and E is an injective module. Also, we prove that over a quasi-complete Noetherian ring (R, \frak m) an R-module D is cyclically pure injective if and only if there is a family {Cλ}λ ∈ Λ of cocyclic modules such that D is isomorphic to a direct summand of Πλ ∈ ΛCλ. Finally, we show that over a complete local ring every finitely generated module which has small cofinite irreducibles is cyclically pure injective.

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