Algebra over a commutative ring

Set

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 $[z,r\cdot x+s\cdot y]=r\cdot [z,x]+s\cdot [z,y]$

Discussion

Reference

Wikipedia: Algebra (Ring theory)

Parents

Refinement of

Module