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left_module_homomorphism [2013/08/31 14:46] nikolaj |
left_module_homomorphism [2014/03/21 11:11] (current) |
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===== Left module homomorphism ===== | ===== Left module homomorphism ===== | ||
- | ==== Definition ==== | + | ==== Set ==== |
- | | @#88DDEE: $M,N$...left $\mathcal R$-module | | + | | @#55CCEE: context | @#55CCEE: $M,N$...left $\mathcal R$-module | |
- | | @#FFBB00: $A\in \mathrm{Hom}_{\mathcal R}(M,N)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $A\in \mathrm{Hom}_{\mathcal R}(M,N)$ | |
- | | @#88DDEE: $A:M\to N$ | | + | | @#55CCEE: context | @#55CCEE: $A:M\to N$ | |
- | | @#55EE55: $A\ (r\cdot x+s\cdot y)=r\cdot A\ x+s\cdot A\ y$ | | + | | @#55EE55: postulate | @#55EE55: $A\ (r\cdot x+s\cdot y)=r\cdot A\ x+s\cdot A\ y$ | |
==== Discussion ==== | ==== Discussion ==== | ||
==== Reference ==== | ==== Reference ==== | ||
Wikipedia: [[https://en.wikipedia.org/wiki/Left_module#Submodules_and_homomorphisms|Module]] | Wikipedia: [[https://en.wikipedia.org/wiki/Left_module#Submodules_and_homomorphisms|Module]] | ||
- | ==== Context ==== | + | ==== Parents ==== |
- | === Requirements === | + | === Context === |
[[Left module]] | [[Left module]] |