| context | $A$…R-module |
| postulate | $\langle A,[\cdot,\cdot]\rangle \in \mathrm{algebra}(A)$ |
| context | $[\cdot,\cdot] : A\times A\to A$ |
| $x,y,z\in A$ |
| $r,s\in R$ |
Bilinearity:
| postulate | $[r\cdot x+s\cdot y,z]=r\cdot [x,z]+s\cdot [y,z]$ |
| postulate | $[z,r\cdot x+s\cdot y]=r\cdot [z,x]+s\cdot [z,y]$ |
Wikipedia: Algebra (Ring theory)