Chevalley scheme

A Chevalley scheme in algebraic geometry was a precursor notion of scheme theory.

Let X be a separated integral noetherian scheme, R its function field. If we denote by ${\displaystyle X'}$ the set of subrings ${\displaystyle {\mathcal {O}}_{x}}$ of R, where x runs through X (when ${\displaystyle X=\mathrm {Spec} (A)}$, we denote ${\displaystyle X'}$ by ${\displaystyle L(A)}$), ${\displaystyle X'}$ verifies the following three properties

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