R-module homomorphism

An $R$-module homomorphism is an additive map $f:M\to N$ satisfying $f(rm)=rf(m)$.

The endomorphism ring ${\mathrm{End}}_R(M)$ consists of the $R$-module homomorphisms $M\to M$, with pointwise addition and composition as multiplication.

A nonzero module is a brick when every endomorphism is either zero or an isomorphism. Equivalently, its endomorphism ring is a division ring.