# Thread: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

1. ## Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

I need to prove that this two rings are isomorphic.
$A[X_1,X_2,,,X_n]\simeq A[X_1,X_2,,,X_{n-1}][X_n]$

b) what are the element of $A[X_1,X_2,,,X_{n-1}][X_n]$ ?

Thank YOU

2. ## Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

Is this about polynomials? Then $A[X_1,\dots,X_{n-1}][X_n]$ consists of polynomials of $X_n$ whose coefficients are polynomials of $X_1,\dots,X_{n-1}$. It is clear that ultimately such thing is a polynomial of $X_1,\dots,X_{n}$.

3. ## Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

Yes they are RINGS POLYNOMIALS.

4. ## Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

what are the element of A[X1,,Xn-1][Xn] ?