Progenerator

Summary

A progenerator over a ring $R$ is a finitely generated projective module that is also a generator of the module category. The free modules $R^n$ with $n \ge 1$ are progenerators. Progenerators are the modules that control Morita equivalence. A ring $S$ is Morita equivalent to $R$ exactly when it is the endomorphism ring of a progenerator over $R$. This holds up to the choice of side.