FACTOR CATEGORIES AND INFINITE DIRECT SUMS

Abstract

We give an improved categorical version of the Weak Krull-Schmidt Theorem for serial modules proved by the second author in [10]. The main improvement consists in the fact that it applies not only to serial modules, but also, more generally, to arbitrary direct summands of serial modules. The technique is based on categorical methods, essentially representing the category add(SUsr) of direct summands of serial modules into factors of the category add(SUsr) modulo suitable ideals, one for each uniserial module of type 1 and two for each uniserial module of type 2. Our categorical technique can be applied to further broader settings.

Keywords

• Uniserial modules, serial modules, direct-sum decompositions