Define 3 Show That I Is Algebraic 4 8 Over Q Hint Theorem Let T Be A Commutative Ring And Let S Be A Su 1 (11.74 KiB) Viewed 41 times
Theorem 4.8
Define 3 Show That I Is Algebraic 4 8 Over Q Hint Theorem Let T Be A Commutative Ring And Let S Be A Su 2 (31.36 KiB) Viewed 41 times
Define : +√-3. Show that (+i is algebraic = 4.8.] over Q. [Hint: Theorem
Let T be a commutative ring, and let S be a subring of T. Then IT (S) is a subring of T. PROOF. Let p and q be elements in IT (S), and set A = {p, q}. Then, by Proposition 4.6, S[A] ≤ IT(S). Since p, q E S[A] and S[A] is a subring of T, p-q E S[A] and pq E S[A]. Thus, p-q IT(S) and pq € IT(S).
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