Indecomposable modules over right pure semisimple rings (Q1098915)

Let A be a right pure semisimple ring. It is well known that every indecomposable right A-module is finitely generated, and that there are at most \(| A| +\aleph_ 0\) indecomposable right modules. In this paper we prove (with the aid of ultraproduct-technique) that A satisfies one of the two following statements: (a) For any positive integer n, there are at most finitely many indecomposable right modules of length n; or (b) There is an infinite number of integers d such that, for each d, A has infinitely many indecomposable right modules of length d.