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
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
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 $\displaystyle X_1,\dots,X_{n}$.