# The Stacks Project

## Tag 00JN

Definition 10.56.1. Let $S$ be a graded ring. We define $\text{Proj}(S)$ to be the set of homogeneous prime ideals $\mathfrak p$ of $S$ such that $S_{+} \not \subset \mathfrak p$. The set $\text{Proj}(S)$ is a subset of $\mathop{\rm Spec}(S)$ and we endow it with the induced topology. The topological space $\text{Proj}(S)$ is called the homogeneous spectrum of the graded ring $S$.

The code snippet corresponding to this tag is a part of the file algebra.tex and is located in lines 12754–12764 (see updates for more information).

\begin{definition}
\label{definition-proj}
Let $S$ be a graded ring.
We define $\text{Proj}(S)$ to be the set of homogeneous
prime ideals $\mathfrak p$ of $S$ such that
$S_{+} \not \subset \mathfrak p$.
The set $\text{Proj}(S)$ is a subset of $\Spec(S)$
and we endow it with the induced topology.
The topological space $\text{Proj}(S)$ is called the
{\it homogeneous spectrum} of the graded ring $S$.
\end{definition}

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