Abstract
For a Quillen exact category \({\mathcal {C}}\) endowed with two exact structures \({\mathcal {D}}\) and \({\mathcal {E}}\) such that \({\mathcal {E}}\subseteq {\mathcal {D}}\), an object X of \({\mathcal {C}}\) is called \({\mathcal {E}}\)-divisible (respectively \({\mathcal {E}}\)-flat) if every short exact sequence from \({\mathcal {D}}\) starting (respectively ending) with X belongs to \({\mathcal {E}}\). 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Applicable Algebra in Engineering, Communication and Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.