Let (= e²mi/3 = −¹+√-3 EC and consider the ring 2 Z[S] = {a + bc | a,b ≤ Z}. (a) Define a ring homomorphism y: Z[S] → Z/

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Let E Mi 3 3 Ec And Consider The Ring 2 Z S A Bc A B Z A Define A Ring Homomorphism Y Z S Z 1 (88.66 KiB) Viewed 41 times

Let (= e²mi/3 = −¹+√-3 EC and consider the ring 2 Z[S] = {a + bc | a,b ≤ Z}. (a) Define a ring homomorphism y: Z[S] → Z/7Z. Prove that your function is a ring homomorphism. (b) Determine the kernel of the homomorphism you constructed in the previous part. Give your answer in the form of an ideal generated by the minimum possible number of gener- ators this ideal can have.