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Consider the ring Z[x] and let J = ãx + 1ã Explain why J is prime. Show that J is not maximal Conclude that Z [x]/J is an integral domain but not a field. Observe that/ is the kernel of the evaluation homomorphism Ï-1 : Z[ì§ â Z. Consequently, Z [x]/JZ by the first isomorphism theorem for rings.
Consider the ring Z[x] and let J = ãx + 1ã Explain why J is prime. Show that J is not maximal Conclude that Z [x]/J is an integral domain but not a field. Observe that/ is the kernel of the evaluation homomorphism Ï-1 : Z[ì§ â Z. Consequently, Z [x]/JZ by the first isomorphism theorem for rings.
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Bunny GreenfelderLv2
22 Jan 2019