If R has an identity, then (a) J(R) r R I 1 R s r is left invertible for all s R (b) J(R) is the largest ideal K such that for all r K, 1 R r is a unit ...

Lets prove both parts a First lets show that JR is contained in the set r R 1R sr is left invertible for all s R Let r be an element of JR which means that for every s R 1R sr is left invertible This ...

If R has an identity, then (a) J(R) = {r R I 1 R + s

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If R has an identity, then

(a) J(R) = {r ϵ R I 1_R + s_r is left invertible for all s ϵ R}.

(b) J(R) is the largest ideal K such that for all r ϵ K, 1_R + r is a unit.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Aug 03, 2023 08:28 AM

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If R has an identity, then (a) J(R) = {r R I 1 R + s

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Lets prove both parts a First lets show that JR is contained in the set r R 1R sr is left invertible for all s R Let r be an element of JR which means that for every s R 1R sr is left invertible This ...View the full answer

Algebra Graduate Texts In Mathematics 73

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