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 1R + sr is left invertible for all s ϵ R}.
(b) J(R) is the largest ideal K such that for all r ϵ K, 1R + r is a unit.
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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
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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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