Let R be a ring without identity and with no zero divisors Let S be the ring whose additive group is R X Z as in the proof of Theorem 1 10 Let A (r,n) S rx nx O for every x R (a) A is an ideal in S (b) S A has an identity and contains a subring isomorphic to R (c) S A has no zero divisors ...

a To show that A is an ideal of S we need to verify that for any rn and sm in A and any xy in S we h ...

Let R be a ring without identity and with no zero divisors. Let S be the ring

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Let R be a ring without identity and with no zero divisors. Let S be the ring whose additive group is R X Z as in the proof of Theorem 1.10. Let A= {(r,n) ϵ S|rx+nx = O for every x ϵ R}.

(a) A is an ideal in S.

(b) S/ A has an identity and contains a subring isomorphic to R.

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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 16, 2023 03:56 AM

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Let R be a ring without identity and with no zero divisors. Let S be the ring

Question:

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a To show that A is an ideal of S we need to verify that for any rn and sm in A and any xy in S we h...View the full answer

Algebra Graduate Texts In Mathematics 73

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