I found statement of theorem, that for any field $F$, any homomorphism $f:GL(n, F)\rightarrow F^{*}$ is composition $f=g\circ det$ for some $g:F^{*}\rightarrow F^{*}$ - endomorphism, and $det$ - determinant. But i could'n find proof of that theorem, could you help?
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Homomorphism of what? – azif00 Aug 15 '23 at 05:34
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@azif00 of general linear group over F and F* - multiplicative group of F – nagvalhm Aug 15 '23 at 05:38
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@Mariano Suárez-Álvarez, but how is determinant coming out here? – nagvalhm Aug 15 '23 at 05:51