More on abundance of cosilting modules
Volume 172 / 2023
Colloquium Mathematicum 172 (2023), 31-47
MSC: Primary 16D90; Secondary 18E10, 16D10, 18G15.
DOI: 10.4064/cm8683-4-2022
Published online: 10 October 2022
Abstract
Let be a ring. We give a characterization of cosilting modules and establish a relation between cosilting modules and cotilting objects in a certain Grothendieck category. We show that each cosilting right R-module T can be described as a cotilting object in \sigma [R/I], where I is a right ideal of R determined by T and \sigma [R/I] is the full subcategory of right R-modules, consisting of submodules of modules generated by R/I. Conversely, under some suitable homological vanishing conditions, if T is a cotilting object in \sigma [R/I], then T is cosilting.
