In An Introduction To Groebner Bases from Loustaunau, it says that:
We further note that the Noetherian property of the ring R, and hence of the ring $R[x_1, \dots, x_n]$, yields to the following Corollary, whose proof we leave to the exercises. Corollary 4.1.17: Let $I$ in $R[x_1, \dots, x_n]$ be a non-zero ideal, then $I$ has a finite Groebner basis.
I need to demonstrate this corollary, existence of Groebner bases in $R[x_1, ..., x_n]$, but I am not sure how. We are asuming that $R$ is a Noetherian ring. Can someone give the proof or refer to somewhere where I can find it? Thanks in advance!