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 : R \to R [x]

by

r \mapsto r

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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