Some criteria of cyclically pure injective modules

Details Some criteria of cyclically pure injective modules Some criteria of cyclically pure injective modules

2005-10-20

arxiv.org/abs/math/0510433v1

Mathematics

Commutative Algebra

18 pages, to appear in Journal of Algebra

Scientific paper

The structure of cyclically pure injective modules over a commutative ring $R$ is investigated and several characterizations 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 $(R,\fm)$ an $R$-module $D$ is cyclically pure injective if and only if there is a family $\{C_\lambda\}_{\lambda\in \Lambda}$ of cocyclic modules such that $D$ is isomorphic to a direct summand of $\Pi_{\lambda\in \Lambda}C_\lambda$. Finally, we show that over a complete local ring every finitely generated module which has small cofinite irreducibles is cyclically pure injective.

Affiliated with

Also associated with

No associations

Rating

Some criteria of cyclically pure injective modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some criteria of cyclically pure injective modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some criteria of cyclically pure injective modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-476014