(a) If R 1 . ... , R n are rings with identity and I is an...

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(a) If R₁. ... , R_n are rings with identity and I is an ideal in R₁ X --· X R_n, then I = A₁ X · · · X A_m, where each A_i is an ideal in R_i.

(b) Show that the conclusion of (a) need not hold if the rings R_i do not have identities.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:04 AM

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(a) If R 1 . ... , R n are rings with identity and I is an...

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ANSWER a Suppose that R1 Rn are rings with identity and let I be an ideal in R1 x x Rn Let i R1 x x ...View the full answer

Algebra Graduate Texts In Mathematics 73

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