If $A/I$ is a d-dimensional local ring, and $I$ is generated by $h$ elements, can we have the conclusion that dim A $\leq h+d$ ?
I was actually reading Commutative ring theory by Matsumura. And my problem is on p.120 the proof of theorem 12.6, The inequality right before the last paragraph. I am not really sure the inequality came from the construction in the proof or just the statement I proposed.
Thanks for answering!