Valuation domains with a maximal immediate extension of finite rank

Details Valuation domains with a maximal immediate extension of finite rank Valuation domains with a maximal immediate extension of finite rank

2009-01-12

arxiv.org/abs/0901.1651v1

Journal of Algebra 323, 1 (2010) 32-41

Mathematics

Rings and Algebras

Scientific paper

If $R$ is a valuation domain of maximal ideal $P$ with a maximal immediate extension of finite rank it is proven that there exists a finite sequence of prime ideals $P=L_0\supset L_1\supset...\supset L_m\supseteq 0$ such that $R_{L_j}/L_{j+1}$ is almost maximal for each $j$, $0\leq j\leq m-1$ and $R_{L_m}$ is maximal if $L_m\ne 0$. Then we suppose that there is an integer $n\geq 1$ such that each torsion-free $R$-module of finite rank is a direct sum of modules of rank at most $n$. By adapting Lady's methods, it is shown that $n\leq 3$ if $R$ is almost maximal, and the converse holds if $R$ has a maximal immediate extension of rank $\leq 2$.

Affiliated with

Also associated with

No associations

Rating

Valuation domains with a maximal immediate extension of finite rank 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 Valuation domains with a maximal immediate extension of finite rank, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Valuation domains with a maximal immediate extension of finite rank will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-71038