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 Sep15 awarded Nice Question Jul2 awarded Curious Jun14 awarded Popular Question Jun20 awarded Yearling Apr21 comment Algebraic group homomorphism well,I need to think about it. Apr21 comment Algebraic group homomorphism Yes,agree.So it should be that there exist $P \in GL_{n}(\mathbb C)$ such that $P\phi(G_{m})P^{-1}$ lies in the diagonal matrices.Certainly there exist $P$ such that $P\phi(G_{m})P^{-1}$ lies in set of all upper triangular matrices. Apr21 suggested rejected edit on Can $C_{10}$ be isomorphic to $C_5\times C_2$? Apr21 asked Algebraic group homomorphism Feb6 comment Irreducible element of the ring. @Sarjbak: thanks for your nice solution. Feb4 accepted dimension of image of proper closed set under a morphism. Feb4 comment dimension of image of proper closed set under a morphism. Sorry I got your idea as restriction of a finite morphism on a closed set is finite. Feb4 comment dimension of image of proper closed set under a morphism. sorry,I did not get your idea completely.I can show that if $\pi$ is finite surjective morphism from irreducible to irreducible ,then dim$X=$dim$Y$.But why should restriction of finite morphism finite? Feb4 comment dimension of image of proper closed set under a morphism. I am sorry that i am not aware of base-scheme Jacobson?But I think now question is clear to you. Feb4 revised dimension of image of proper closed set under a morphism. added 15 characters in body Feb4 asked dimension of image of proper closed set under a morphism. Feb3 accepted Irreducible element of the ring. Feb2 revised Irreducible element of the ring. added 13 characters in body Feb2 comment Irreducible element of the ring. Sorry forget to mention ,now I have corrected it. Feb2 revised Irreducible element of the ring. added 21 characters in body Feb2 asked Irreducible element of the ring.