Indecomposables live in all smaller lengths

Details Indecomposables live in all smaller lengths Indecomposables live in all smaller lengths

2009-12-26

arxiv.org/abs/0912.5002v2

Mathematics

Representation Theory

Scientific paper

Let $\Lambda$ be a finite-dimensional $k$-algebra with $k$ algebraically closed. Bongartz has recently shown that the existence of an indecomposable $\Lambda$-module of length $n > 1$ implies that also indecomposable $\Lambda$-modules of length $n-1$ exist. Using a slight modification of his arguments, we strengthen the assertion as follows: If there is an indecomposable module of length $n$, then there is also an accessible one. Here, the accessible modules are defined inductively, as follows: First, the simple modules are accessible. Second, a module of length $n \ge 2$ is accessible provided it is indecomposable and there is a submodule or a factor module of length $n-1$ which is accessible.

Affiliated with

Also associated with

No associations

Rating

Indecomposables live in all smaller lengths 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 Indecomposables live in all smaller lengths, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Indecomposables live in all smaller lengths will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-122268