Morita-equivalent modules

Definition

Definition with symbols

Two modules $M_1$ and $M_2$ over a commutative unital ring are said to be Morita-equivalent if there are projective modules $P_1$ and $P_2$ such that:

$M_1\oplus P_1\cong M_2\oplus P_2$

Modules, modulo the relation of Morita equivalence, give rise to the Morita category.