Free submodules of indecomposable modules. (Q1881016)

Let \(\Lambda\) be an Artin algebra. It is proved that if \(\Lambda\) has only finitely many isomorphism classes of non-faithful indecomposable modules, then for each natural number \(t\), there is a bound \(b_t\) such that any indecomposable \(\Lambda\)-module of length at least \(b_t\) contains a free submodule of rank \(t\). As a consequence, if there are infinitely many non-isomorphic modules of length \(t\), then any indecomposable \(\Lambda\)-module of length at least \(b_t\) has infinitely many isomorphism classes of subfactors. The author gives several remarks on connections between the results of the paper and the second Brauer-Thrall conjecture. He also proposes the following conjecture: If \(\Lambda\) is an infinite Artin algebra of infinite representation type, then there exists a bound \(b\) such that any indecomposable module of length greater than \(b\) contains infinitely many isomorphism classes of subfactors.