Hi,
I want to prove the following theorem
"If $R[x_1,...,x_n]$ denotes a polynomial ring in n variables, then $gl.dim(R[x_1,...,x_n])=n+gl.dim(R)$"
(gl.dim = global dimension)
I already have the proof for R[x] and want to ask if my following calculation is right
$gl.dim(R[x_1,...,x_{n+1}])=gl.dim(R[x_1,...,x_n][x_{n+1}])=1+gl.dim(R[x_1,...,x_n])=$ $=1+gl.dim(R[x_1,...,x_{n-1}][x_n])=...$
It seems to me that it is to easy...
Thank you!
