| context | $X$…left $\mathcal R$-module |
| definiendum | $\langle \mathrm{Hom}(X,X),+,\cdot,*,\rangle \in L(X,X)$ |
| context | $\langle \mathrm{Hom}(X,X),+,\cdot\rangle \in \mathcal L(X,X)$ |
| context | $*:\mathrm{Hom}(X,X)\times \mathrm{Hom}(X,X)\to \mathrm{Hom}(X,X)$ |
| $ v\in M $ |
| $A,B \in \mathrm{Hom}(X,Y)$ |
| postulate | $(A*B)v = A(B v) $ |
Theorem: A linear operator $A:X\to X$ is bijective if it has an inverse in $L(X,X)$.