I need to prove that this two rings are isomorphic.

$\displaystyle $A[X_1,X_2,,,X_n]\simeq A[X_1,X_2,,,X_{n-1}][X_n]$$

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

Thank YOU

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- Jul 9th 2013, 08:26 AMjohn27Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
I need to prove that this two rings are isomorphic.

$\displaystyle $A[X_1,X_2,,,X_n]\simeq A[X_1,X_2,,,X_{n-1}][X_n]$$

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

Thank YOU - Jul 9th 2013, 12:09 PMemakarovRe: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
Is this about polynomials? Then $\displaystyle A[X_1,\dots,X_{n-1}][X_n]$ consists of polynomials of $\displaystyle X_n$ whose coefficients are polynomials of $\displaystyle X_1,\dots,X_{n-1}$. It is clear that ultimately such thing is a polynomial of $\displaystyle X_1,\dots,X_{n}$.

- Jul 9th 2013, 01:56 PMjohn27Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
Yes they are RINGS POLYNOMIALS.

- Jul 10th 2013, 09:21 AMjohn27Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]
what are the element of A[X1,,Xn-1][Xn] ?