Ring Theory Seminar

Hongdi Huang, Pure Mathematics, University of Waterloo

"Morita Theory IV: The Morita Context"

If $F:\mathrm{Mod}_R \rightarrow \mathrm{Mod}_S$ is a Morita equivalence, then it preserves progenerators, so $P_S:= F(R_R)$ is a progenerator in $\mathrm{Mod}_S$. We'll see that that $P_S$ has a left $R$-module structure and $F\simeq -\otimes _RP_S$, thus giving rise to a \textit{Morita context} between $R$ and $S$. Conversely, the existence of a Morita context implies that $R$ and $S$ are Morita equivalent.