Let R be a ring without identity. Embed Rina ring S with identity and characteristic zero as
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Let R be a ring without identity. Embed Rina ring S with identity and characteristic zero as in the proof of Identify R with its image in S.
(a) Show that every element of S may be uniquely expressed in the form r1s + n1s (r ϵ R, n ϵ Z).
(b) If A is an R-module and a ϵ A, show that there is a unique R-module homomorphism ∫: S → A such that ∫(1s) = a.
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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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