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algebra_over_a_commutative_ring [2013/08/31 17:21] nikolaj created |
algebra_over_a_commutative_ring [2013/08/31 17:27] nikolaj |
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| | @#55EE55: $\langle A,[\cdot,\cdot]\rangle \in \mathrm{algebra}(A)$ | | | @#55EE55: $\langle A,[\cdot,\cdot]\rangle \in \mathrm{algebra}(A)$ | | ||
| - | | @#88DDEE: $[\cdot,\cdot]: A\times A\to A\$ | | + | | @#88DDEE: $[\cdot,\cdot] : A\times A\to A$ | |
| | $x,y,z\in A$ | | | $x,y,z\in A$ | | ||
| | $r,s\in R$ | | | $r,s\in R$ | | ||
| + | |||
| + | Bilinearity: | ||
| | @#55EE55: $[r\cdot x+s\cdot y,z]=r\cdot [x,z]+s\cdot [y,z]$ | | | @#55EE55: $[r\cdot x+s\cdot y,z]=r\cdot [x,z]+s\cdot [y,z]$ | | ||
