# Prime ideal structure in commutative rings

@article{Hochster1969PrimeIS, title={Prime ideal structure in commutative rings}, author={Melvin Hochster}, journal={Transactions of the American Mathematical Society}, year={1969}, volume={142}, pages={43-60} }

0. Introduction. Let ' be the category of commutative rings with unit, and regard Spec (as in [1]) as a contravariant functor from ' to g$7 the category of topological spaces and continuous maps. The spaces of the form Spec A, A a ring (ring always means object of '), are well known to have many special properties. It is worthwhile to discover whether these well-known properties of the spaces characterize them, since we then will know the limitations of the topological approach. As a by-product…

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## References

### Rings of continuous functions

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Contents: Functions of a Topological Space.- Ideals and Z-Filters.- Completely Regular Spaces.- Fixed Ideals. Compact Spaces.- Ordered Residue Class Rings.- The Stone-Czech Compactification.-…