nLab
Hochster duality

Contents

Contents

Idea

Given a coherent space, XX, a new topology may be constructed by taking as basic open subsets the closed sets of XX with quasicompact complements. This space X X^{\vee} is called the Hochster dual of XX. The space X X^{\vee} is also coherent and X =XX^{\vee \vee} = X.

The Hochster dual of a distributive lattice is the opposite lattice. The Hochster dual of a coherent frame is its join completion.

References

The original source is

  • M. Hochster, Prime ideal structure in commutative rings, Transactions of the American Mathematical Society, 142, (1969), 43–60

See also:

Last revised on May 19, 2020 at 13:27:11. See the history of this page for a list of all contributions to it.