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| Paper IPM / M / 7993 |
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| Abstract: | |||||||
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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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