Lemma 10.57.8 (00JU)—The Stacks project

Processing math: 100%

Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.57: Proj of a graded ring
Lemma 10.57.8 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 10.57.8. Let $S$ be a graded ring.

Any minimal prime of $S$ is a homogeneous ideal of $S$ .
Given a homogeneous ideal $I \subset S$ any minimal prime over $I$ is homogeneous.

Proof. The first assertion holds because the prime $\mathfrak q$ constructed in Lemma 10.57.7 satisfies $\mathfrak q \subset \mathfrak p$ . The second because we may consider $S/I$ and apply the first part. $\square$

Comments (0)

There are also:

7 comment(s) on Section 10.57: Proj of a graded ring

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment