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Tag 00JN

Chapter 10: Commutative Algebra > Section 10.56: Proj of a graded ring

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 $\mathop{\mathrm{Spec}}(S)$ 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 12757–12767 (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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