Abstract
In this chapter we will put a topology on Kn and on affine varieties. This topology is quite weak, but surprisingly useful. We will define an analogous topology on Spec(R). In both cases, there are correspondences between closed sets and radical ideals. As a consequence of some general topological con siderations, affine varieties can be decomposed into irreducible components. Another consequence is that a Noetherian ring contains only finitely many minimal prime ideals.
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© 2011 Springer-Verlag Berlin Heidelberg
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Kemper, G. (2011). The Zariski Topology. In: A Course in Commutative Algebra. Graduate Texts in Mathematics, vol 256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03545-6_4
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DOI: https://doi.org/10.1007/978-3-642-03545-6_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03544-9
Online ISBN: 978-3-642-03545-6
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