Differences
This shows you the differences between two versions of the page.
algebra_over_a_commutative_ring [2013/08/31 17:27] nikolaj |
algebra_over_a_commutative_ring [2014/03/21 11:11] |
||
---|---|---|---|
Line 1: | Line 1: | ||
- | ===== Algebra over a commutative ring ===== | ||
- | ==== Definition ==== | ||
- | | @#88DDEE: $A$...R-module | | ||
- | | @#55EE55: $\langle A,[\cdot,\cdot]\rangle \in \mathrm{algebra}(A)$ | | ||
- | |||
- | | @#88DDEE: $[\cdot,\cdot] : A\times A\to A$ | | ||
- | |||
- | | $x,y,z\in A$ | | ||
- | | $r,s\in R$ | | ||
- | |||
- | Bilinearity: | ||
- | |||
- | | @#55EE55: $[r\cdot x+s\cdot y,z]=r\cdot [x,z]+s\cdot [y,z]$ | | ||
- | | @#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)]] | ||
- | ==== Context ==== | ||
- | === Refinement of === | ||
- | [[module]] |