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

• July 9th 2013, 09:26 AM
john27
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
• July 9th 2013, 01:09 PM
emakarov
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 $X_1,\dots,X_{n}$.
• July 9th 2013, 02:56 PM
john27
Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
Yes they are RINGS POLYNOMIALS.
• July 10th 2013, 10:21 AM
john27
Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
what are the element of A[X1,,Xn-1][Xn] ?