Relatively divisible and relatively flat objects in exact categories: applications

Abstract

For a Quillen exact category $${\\mathcal {C}}$$ C endowed with two exact structures $${\\mathcal {D}}$$ D and $${\\mathcal {E}}$$ E such that $${\\mathcal {E}}\\subseteq {\\mathcal {D}}$$ E ⊆ D , an object X of $${\\mathcal {C}}$$ C is called $${\\mathcal {E}}$$ E -divisible (respectively $${\\mathcal {E}}$$ E -flat) if every short exact sequence from $${\\mathcal {D}}$$ D starting (respectively ending) with X belongs to $${\\mathcal {E}}$$ E . We continue our study of relatively divisible and relatively flat objects in Quillen exact categories with applications to finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.