Definition:Transitive Reduction/Relation Theory

Definition
Let $\RR$ be a relation on a set $S$.

A transitive reduction of $\RR$ is denoted $\RR^-$, and is defined as a minimal relation on $S$ which has the same transitive closure as $\RR$.

Also see

 * Transitive Reduction Exists if Transitive Closure Antisymmetric and Finite