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More on abundance of cosilting modules

Volume 172 / 2023

Yonggang Hu, Panyue Zhou Colloquium Mathematicum 172 (2023), 31-47 MSC: Primary 16D90; Secondary 18E10, 16D10, 18G15. DOI: 10.4064/cm8683-4-2022 Published online: 10 October 2022


Let $R$ 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.


  • Yonggang HuDepartment of Mathematical Sciences
    Tsinghua University
    100084 Beijing, P.R. China
  • Panyue ZhouSchool of Mathematics and Statistics
    Changsha University of Science and Technology
    410114 Changsha, Hunan, P.R. China

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