Let R be a commutative ring. Show that R[x] has a subring isomorphic to R.

defazajx 2020-12-21 Answered
Let R be a commutative ring. Show that R[x] has a subring isomorphic to R.
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joshyoung05M
Answered 2020-12-22 Author has 97 answers
Let R be a commutative rng and consider R[x]
Define: ϕ:RR[x] by rr
Here, clearly we can say that ϕ is one-to-one and homomorphism
Now, ϕ(R) is subsring of R[x] since it is the imag of a homomorphism
Then ϕ(R) is subsring of R[x] isomorphic to R
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