(a) Define a homomorphism : Zx Z→ Z with Ker = ((0, 1)). Show complete details. (b) Verify that is onto. (c) Use FIT for rings to show that Z/ ((0,1)) ≈Z. ZxZ

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A: We are given : f(x)=x3+x2+x+0⇒f(x)=x3+x2+xand g(x)=x+[1]⇒g(x)=x+1Now, Dividing f(x) by  g(x), we…

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A: Let x, y ∈ R. Then (fg)(x + y) = f(g(x + y)) = f(g(x) + g(y)) = f(g(x)) + f(g(y)) =(fg)(x)+(fg)(y),…

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Q: Leto: R₁ R₂ be a homomorphism of rings. Show that the mapping o': R₁[x] → R₂[r] given by o(am…

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