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

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

    Yes they are RINGS POLYNOMIALS.
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    Re: Prove that A[X1,,,Xn] isomorphic with A[X1,,,Xn-1][Xn]

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