J. Aust. Math. Soc.
79 (2005), 349360

Modules which are invariant under monomorphisms of their injective hulls

A. Alahmadi
Department of Mathematics
Ohio University
Athens, OH 45701
USA
noyaner@yahoo.com


N. Er
Department of Mathematics
The Ohio State UniversityNewark
OH 43055
USA



S. K. Jain
Department of Mathematics
The Ohio State UniversityNewark
OH 43055
USA



Abstract

In this paper certain injectivity conditions in
terms of extensions of monomorphisms are
considered. In particular, it is proved that a
ring is a quasiFrobenius ring if and only if every
monomorphism from any essential right ideal of
into
can be extended to
. Also, known results on pseudoinjective modules
are extended. Dinh raised the question if a
pseudoinjective CS module is quasiinjective.
The following results are obtained:
is quasiinjective if and only if
is pseudoinjective and
is CS. Furthermore, if
is a direct sum of uniform modules, then
is quasiinjective if and only if
is pseudoinjective. As a consequence of this it
is shown that over a right Noetherian ring
, quasiinjective modules are precisely
pseudoinjective CS modules.

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