1 Define 2 3 Show That I Is Algebraic Over Q Hint Theorem 4 8 Let T Be A Commutative Ring And Let S Be 1 (22.88 KiB) Viewed 23 times
1 Define : +2√-3. Show that +i is algebraic over Q. [Hint: Theorem ( − 4.8.]
Let T be a commutative ring, and let S be a subring of T. Then IȚ(S) is a subring of T. be elements in IȚ(S), and set A := = {p,q}. Then, by Proposition 4.6, PROOF. Let P and q S[A] ≤ IT(S). Since p, q € S[A] and S[A] is a subring of T, p− q € S[A] and pq € S[A]. Thus, p − q = It(S) and pq E IT(S).
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