Left orthogonal classes of semidualizing bimodules
Volume 165 / 2021
Colloquium Mathematicum 165 (2021), 103-116
MSC: Primary 18G25.
DOI: 10.4064/cm8294-9-2020
Published online: 14 December 2020
Abstract
Let $R$ be a left coherent ring and $S$ a right coherent ring, and let $_RC_S$ be a semidualizing bimodule. We show that the class $\mathcal {T}_C(R)$ of finitely presented $\infty $-$C$-torsionfree left $R$-modules satisfies the two-out-of-three property relative to $C$-coproper short exact sequences. In addition, we give some equivalent characterizations when there is an inclusion relation between $\mathcal {T}_C(R)$ and the left orthogonal class of $_RC$.
