Let S and R' be disjoint rings with the property that S contains a subring S' such that there is an isomorphism f' of S' onto R'. Prove that there is a ring R containing R' and an isomorphism f of S onto R such that f' = f\s¹.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Abstract Algebra: Embedding of rings 

Let S and R' be disjoint rings with the property that S contains a subring
S' such that there is an isomorphism f' of S' onto R'. Prove that there
is a ring R containing R' and an isomorphism f of S onto R such that
f' = f\s¹.
Transcribed Image Text:Let S and R' be disjoint rings with the property that S contains a subring S' such that there is an isomorphism f' of S' onto R'. Prove that there is a ring R containing R' and an isomorphism f of S onto R such that f' = f\s¹.
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