$H=\left\{ \begin{bmatrix} a & b \\ 0 & c \end{bmatrix}:a,b,c\in Z\right\}$ get the ring $\varphi :H\rightarrow Z$ , $\varphi \left( \begin{bmatrix} a & b \\ 0 & c \end{bmatrix}\right) =c$ Does the transformation become a ring homomorphism? Essays: $\varphi \left( \begin{bmatrix} a & b \\ 0 & c \end{bmatrix}+\begin{bmatrix} d & e \\ 0 & f \end{bmatrix}\right)=\varphi \left( \begin{bmatrix} a & b \\ o & c \end{bmatrix}\right) +\varphi \left( \begin{bmatrix} d & e \\ 0 & f \end{bmatrix}\right)$ because $c\neq 2c$ there is no homomorphism with interest, right? Is there something I can't see?
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$fi(A+B)=c+f=fi(A)+fi(B)$ – hamam_Abdallah May 26 '20 at 22:28
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When you write $\varphi \left( \begin{bmatrix} a & b \ 0 & c \end{bmatrix}\right) =c$, the $c$ in the RHS is the same $c$ as in the LHS. – May 26 '20 at 22:29
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@Gae.S. I do not understand – Yusuf Kanat May 26 '20 at 22:32
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@YusufKanat I figured as much. – May 26 '20 at 22:33
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can you solve it? – Yusuf Kanat May 26 '20 at 22:35
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where does $2c$ come from $? c\ne 2c$ – hamam_Abdallah May 26 '20 at 22:35
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You get $c+f$ on both sides. Where does this $2c$ come from? – Berci May 26 '20 at 22:39
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@hamam_Abdallah $\varphi \left( \begin{bmatrix} a & b \ o & c \end{bmatrix}\right) +\varphi \left( \begin{bmatrix} d & e \ 0 & f \end{bmatrix}\right)=2c$ – Yusuf Kanat May 26 '20 at 22:40
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if you solve it i will be very pleased my english is not very good. – Yusuf Kanat May 26 '20 at 22:41
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1Why do you think $\varphi \left( \begin{bmatrix} d & e \ 0 & f \end{bmatrix}\right)=c$? – Noah Schweber May 26 '20 at 23:00
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@NoahSchweber the conversion was given that way – Yusuf Kanat May 26 '20 at 23:17
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@NoahSchweber you perfect man!! – Yusuf Kanat May 26 '20 at 23:20