Let $B$ be a commutative ring and let $\frak p$ be a prime ideal of $B$. Consider a finitely-generated $B$-module $M$.
Let $\mu_{\frak p}(M)$ be the minimal number of generators of $M_{\frak p}$ as a $B_{\frak p}$-module.
Define $e(M)$ to be $\max\{\mu_{\frak p}(M)+\dim B/{\frak p}\mid {\frak p} \text{ is a prime ideal of }B\text{ such that }\dim B/{\frak p}<\dim B\}$.
The aforementioned Eisenbud-Evans conjecture (which was proven by N. Mohan Kumar) says the following:
Let $B=A[T]$ be a polynomial ring in the variable $T$ over the Noetherian ring $A$. Then any finitely-generated $B$-module $M$ can be generated by $e(M)$ elements as a $B$-module.
The aforementioned Forster conjecture says the following:
Let $k$ be a field and let $P$ be a prime ideal in the polynomial ring $S=k[X_1,\dots,X_n]$ such that $S/P$ is regular. Then $P$ can be generated by $n$ elements.
N. Mohan Kumar says it is well-known that the Eisenbud-Evans conjecture implies the Forster conjecture, but does not give a reference.
Can someone please provide the proof? I am interested in an analogue of the Forster conjecture.
Reference
N. Mohan Kumar, "On Two Conjectures about Polynomial Rings," Inventiones Math. 46 (1978), 225-236.