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.
(c) S/ A has no zero divisors.
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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
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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