5. Let f(x) = x' + 1 ( Zy[x] and let R = Za[x]/I, where I = (f(x)). (a) Show that R is a field

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5. Let f(x) = x' + 1 ( Zy[x] and let R = Za[x]/I, where I = (f(x)). (a) Show that R is a field with 9 elements. (b) Denote by 0 := 0 + 1, 1:= 1+ /, and a := r + /. Write the other 6 elements of R terms of o and determine the multiplicative inverse of each nonzero element. (c) Prove that R ~ Za[i]. -end