Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
module [2013/08/31 21:24] nikolaj |
module [2015/12/11 19:48] nikolaj |
||
---|---|---|---|
Line 1: | Line 1: | ||
===== Module ===== | ===== Module ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $M,R$ | | + | | @#55CCEE: context | @#55CCEE: $M,R$ | |
- | | @#55EE55: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{module}(\mathcal M,\mathcal R)$ | | + | | @#55EE55: postulate | @#55EE55: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{module}(\mathcal M,\mathcal R)$ | |
- | | @#88DDEE: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(\mathcal M,\mathcal R)$ | | + | | @#55CCEE: context | @#55CCEE: $\langle\mathcal M,\mathcal R, *\rangle \in \mathrm{leftModule}(\mathcal M,\mathcal R)$ | |
- | | @#88DDEE: $\mathcal M\in \mathrm{abelianGroup}(M)$ | | + | | @#55CCEE: context | @#55CCEE: $\mathcal M\in \mathrm{abelianGroup}(M)$ | |
Now denote the multiplication in the ring $\mathcal R$ by "$\ \hat*\ $". | Now denote the multiplication in the ring $\mathcal R$ by "$\ \hat*\ $". | ||
Line 12: | Line 12: | ||
| $r,s\in R$ | | | $r,s\in R$ | | ||
- | | @#55EE55: $r*s=s*r$ | | + | | @#55EE55: postulate | @#55EE55: $r*s=s*r$ | |
==== Discussion ==== | ==== Discussion ==== | ||
Line 18: | Line 18: | ||
One generally speaks of an $R$-module over $M$. Here $R$ and $M$ are just sets. | One generally speaks of an $R$-module over $M$. Here $R$ and $M$ are just sets. | ||
+ | |||
+ | https://www.youtube.com/watch?v=yZ2dO6Fy5Kc | ||
+ | |||
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Module_%28mathematics%29|Module]] | Wikipedia: [[http://en.wikipedia.org/wiki/Module_%28mathematics%29|Module]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
=== Subset of === | === Subset of === | ||
[[Left module]] | [[Left module]] |