Recent content by wadd

OK. Since f(A)=0 and A is not zero matrix, then Ker(f) has other elements than 0, so our homomorphism can't be injective. So our f can be only surjective now, and I should proof that Im(f) isn't R2. But I haven't any clue how to do that, again.

I did actually think of this, but abandoned because of some brainfart :) If I understood correctly, all I need to do is assume first that there is ring homomomorphism, let it to be f: M2 -> R2. Then f(AB)=f(A)*f(B)=f(B)*f(A)=f(BA), but AB=BA is not universaly true (when A and B are matrices)...

Multiplication in R^2 is defined here: (a, b)*(c, d) = (ac, bd). The homework does not specify properties of homomorphism. The assingment of the homework says also that this can be done without long calculations. If I got it right, I have understood that there is zero homomorphism f: R->S...

Multiplication in R^2 is defined here: (a, b)*(c, d) = (ac, bd). The homework does not specify properties of homomorphism. The assingment of the homework says also that this can be done without long calculations. If I got it right, I have understood that there is zero homomorphism f: R->S only...

Homework Statement Proof that there is no ring homomorphism between M2(R) [2x2 matrices with real elements] and R2 (normal 2-dimensional real plane). Homework Equations -- The Attempt at a Solution I have tried to proof this problem with properties of ring homomorphism (or finding...