Real Algebraic and Analytic Geometry

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71. Marcus Tressl:
Computation of the z-radical in C(X).


Submission: 2004, November 24.

We say that a Tychonoff space X has computable z-radicals if for all ideals I of C(X), the smallest z-ideal containing I is generated as an ideal by all the s(f), where f is in I and s is a continuous function IR-->IR with s-1(0)={0}. We show that every cozero set of a compact space has computable z-radicals and that a subset X of IRn has computable z-radicals if and only if X is locally closed.

Mathematics Subject Classification (2000): 13A10, 46E25, 54C05, 54C40.

Keywords and Phrases: radical, rings of continuous functions, z-ideal.

Full text, 30p.: dvi 181k, ps.gz 210k, pdf 339k.

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