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Abstract algebra-> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with
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[QUOTE="cooljosh2k2, post: 2921887, member: 272421"] [b]Abstract algebra--> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with[/b] [h2]Homework Statement [/h2] Let R be a ring and let M2(R) be the set of 2 x 2 matrices with entries in R. Define a function f by: f(r) = (r 0) <----matrix ...(0 r) for any r ∈ R (a) Show that f is a homomorphism. (b) Find ker(f). [h2]The Attempt at a Solution[/h2] I just want to know if this is right: a) For any r, s in R, f(r) + f(s) = (r 0)..+..(s 0) ....(0 r)...(0 s) = ((r+s) 0) (0 (r+s)) = f(r + s). Therefore, f is a group homomophism. b) ker f = {r ∈ R: f(r) = zero matrix}. This is only possible if r=0. Therefore, ker f = {0} Hence, ker f = {0} [/QUOTE]
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Abstract algebra-> Let R be a ring and let M2(R) be the set of 2 x 2 matrices with
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