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algebra_over_a_commutative_ring [2013/08/31 17:27]
nikolaj
algebra_over_a_commutative_ring [2014/03/21 11:11]
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-===== 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]] 
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