Torsion pairs over n-hereditary rings

DOI10.1080/00927872.2018.1524005zbMATH Open1433.18005arXiv1705.03840OpenAlexW2963813361MaRDI QIDQ5227772

Author name not available (Why is that?)

Publication date: 7 August 2019

Published in: (Search for Journal in Brave)

Abstract: We study the notions of $n$-hereditary rings and its connection to the classes of finitely $n$-presented modules, FP${}_n$-injective modules, FP${}_n$-flat modules and $n$-coherent rings. We give characterizations of $n$-hereditary rings in terms of quotients of injective modules and submodules of flat modules, and a characterization of $n$-coherent using an injective cogenerator of the category of modules. We show two torsion pairs with respect to the FP${}_n$-injective modules and the FP${}_n$-flat modules over $n$-hereditary rings. We also provide an example of a B'ezout ring which is 2-hereditary, but not 1-hereditary, such that the torsion pairs over this ring are not trivial.

Full work available at URL: https://arxiv.org/abs/1705.03840

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Torsion pairs over n-hereditary rings

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5227772)