Difference between revisions of "Characteristic property of the direct sum module/Statement"
From Maths
(Created page with "<noinclude> ==Statement== </noinclude><div style="float:right;margin:0px;margin-left:0.2em;">{{:Characteristic property of the direct sum module/Statement/Picture}}</div><!--...") |
(No difference)
|
Latest revision as of 14:02, 20 October 2016
Statement
- For any family of module homomorphisms, [ilmath](\varphi:M_\alpha\rightarrow M)_{\alpha\in I} [/ilmath]
- There exists a unique module homomorphism, [ilmath]\varphi:\bigoplus_{\alpha\in I}M_\alpha\rightarrow M[/ilmath], such that
- [ilmath]\forall\alpha\in I[\varphi\circ i_\alpha=\varphi_\alpha][/ilmath]
- There exists a unique module homomorphism, [ilmath]\varphi:\bigoplus_{\alpha\in I}M_\alpha\rightarrow M[/ilmath], such that
TODO: Mention commutative diagram and such