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![Exercise 10.3. Given two rings R₁1 and R2, show that (R₁ × R₂)[x] and (R₁[x]) × (R₂[x]) are
isomorphic (as rings).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2e948f6-fd6f-485f-942e-c931230f8579%2Fbf1ee082-d040-4427-adb9-90cebde417d3%2Fmeyn18c_processed.jpeg&w=3840&q=75)
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- b) Find Af(x) if f(x) = (3x+1)(3x+ 4)(3x+7)... (3x+ 19). / c) Let A = {1,2,3}, B = {a, b, c}, and C = {x, y, z}. Consider the following relations R and S from A to B and from B to C, respectively. R = {(1,b), (2,a), (2, c)} and S = {(a, y), (b,x), (c, y), (c, z) }. %3D %3D Find the matrix representation of S°Raw- Let Z[/2] = {a +b/2 |a, b e Z} and let H = { b а 2b : a,b eZ }. a Show that Z[ /2] and H are isomorphic as rings.Consider the ring R = 2Z and the ideal I = 24% of R. Does the ring R/I have an identity? Explain.
