Let R be a ring with no zero divisors such that for all r,s R there

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Let R be a ring with no zero divisors such that for all r,s ϵ R there exist a, b ϵ R, not both zero, with ar + bs = 0.

(a) If R = K⊕L (module direct sum), then K = 0 or L = 0.

(b) If R has an identity, then R has the invariant dimension property.

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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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Let R be a ring with no zero divisors such that for all r,s R there

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a Suppose R KL where K and L are nonzero subrings of R Then we can choose nonzero elements k K and l ...View the full answer

Algebra Graduate Texts In Mathematics 73

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