Mathematics – Commutative Algebra
Scientific paper
2011-08-29
Mathematics
Commutative Algebra
Scientific paper
It is proven that each indecomposable injective module over a valuation domain $R$ is polyserial if and only if each maximal immediate extension $\hat{R}$ of $R$ is of finite rank over the completion $\widetilde{R}$ of $R$ in the $R$-topology. In this case, for each indecomposable injective module $E$, the following invariants are finite and equal: its Malcev rank, its Fleischer rank and its dual Goldie dimension. Similar results are obtained for chain rings satisfying some additional properties. It is also shown that each indecomposable injective module over one Krull-dimensional local Noetherian rings has finite Malcev rank. The preservation of Goldie dimension finiteness by localization is investigated too.
No associations
LandOfFree
Indecomposable injective modules of finite Malcev rank over local commutative rings 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 Indecomposable injective modules of finite Malcev rank over local commutative rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Indecomposable injective modules of finite Malcev rank over local commutative rings will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-127320