A construction of relatively pure submodules

Abstract

We reconsider a classical theorem by Bican and El Bashir, which guarantees the existence of non-trivial relatively pure submodules in a module category over a ring with unit. Our aim is to generalize the theorem to module categories over rings with several objects. As an application we then consider the special case of alpha-pure objects in such module categories.

arXiv comment11 pages, corrected several typos, some references and explanations have been added, two errors in the proof of the main theorem have been corrected, the results remain unchanged