===== Algebra over a commutative ring =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $A$...R-module |

| @#55EE55: postulate   | @#55EE55: $\langle A,[\cdot,\cdot]\rangle \in \mathrm{algebra}(A)$ |

| @#55CCEE: context     | @#55CCEE: $[\cdot,\cdot] : A\times A\to A$ |

| $x,y,z\in A$ |
| $r,s\in R$ |

Bilinearity:

| @#55EE55: postulate   | @#55EE55: $[r\cdot x+s\cdot y,z]=r\cdot [x,z]+s\cdot [y,z]$ |
| @#55EE55: postulate   | @#55EE55: $[z,r\cdot x+s\cdot y]=r\cdot [z,x]+s\cdot [z,y]$ |

==== Discussion ====
=== Reference ===
Wikipedia: [[https://en.wikipedia.org/wiki/Algebra_%28ring_theory%29|Algebra (Ring theory)]]
==== Parents ====
=== Refinement of ===
[[Module]]