Definition 7

An endomorphism e of an A-module E is called a projector if $e \circ e = e$ (in other words, if e is an idempotent in the ring End(E)). In $\operatorname{End}(E)$ a family $(e_\lambda)_{\lambda \in L}$ of projectors is called orthogonal if $e_\lambda \circ e_\mu = 0$ for $\lambda \neq \mu$.