A general theory of structure spaces with applications to spaces of prime ideals
Copyright policy )A general theory of structure spaces with applications to spaces of prime ideals
Let \(R\) be a ring, possibly without an identity element. The join of the Zariski topology on \(\text{Spec}(R)\) and its dual is called the patch topology and is studied here in great detail. In particular the closure in the patch topology of various subspaces of \(\text{Spec}(R)\) is determined such as \(\text{MinSpec}(R)=\) the space of minimal prime ideals and \(\text{MaxSpec}(R)=\) the space of maximal prime ideals. Among other things it is also shown that the patch topology on \(2^ R\) is a compact zero-dimensional Hausdorff space. Its compact subsets are characterized.
- Harvey Mudd College United States
- City College of New York United States
- City University of New York United States
compact zero-dimensional Hausdorff space, maximal prime ideals, minimal prime ideals, Zariski topology, Topological and ordered rings and modules, patch topology, Ideals in associative algebras
compact zero-dimensional Hausdorff space, maximal prime ideals, minimal prime ideals, Zariski topology, Topological and ordered rings and modules, patch topology, Ideals in associative algebras
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