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left_module [2013/08/31 14:37] nikolaj |
left_module [2013/08/31 21:25] nikolaj |
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| @#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 ==== | ||
=== Requirements === | === Requirements === | ||
[[Ring]] | [[Ring]] |