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left_module [2013/08/07 14:19] nikolaj |
left_module [2013/08/31 21:25] nikolaj |
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| | @#88DDEE: $M,R$ | | | @#88DDEE: $M,R$ | | ||
| - | | @#55EE55: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(M,R)$ | | + | | @#FFBB00: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(M,R)$ | |
| | @#88DDEE: $\mathcal M\in \mathrm{abelianGroup}(M)$ | | | @#88DDEE: $\mathcal M\in \mathrm{abelianGroup}(M)$ | | ||
| Line 18: | Line 18: | ||
| | @#55EE55: $(r\ \hat*\ s)* x = r* (s* x)$ | | | @#55EE55: $(r\ \hat*\ s)* x = r* (s* x)$ | | ||
| - | ==== Ramifications ==== | + | ==== Discussion ==== |
| - | === Discussion === | + | |
| "$*$" is an action of the ring on the group from the left. If the ring is commutative, then one need not distinguish between left- and right module. | "$*$" is an action of the ring on the group from the left. If the ring is commutative, then one need not distinguish between left- and right module. | ||
| One generally speaks of an $R$-left-module over $M$. Here $R$ and $M$ are just sets. | One generally speaks of an $R$-left-module over $M$. Here $R$ and $M$ are just sets. | ||
| - | ==== Reference ==== | + | === Reference === |
| Wikipedia: [[http://en.wikipedia.org/wiki/Module_%28mathematics%29|Module]] | Wikipedia: [[http://en.wikipedia.org/wiki/Module_%28mathematics%29|Module]] | ||
| ==== Context ==== | ==== Context ==== | ||
| - | === Parents === | + | === Requirements === |
| [[Ring]] | [[Ring]] | ||
