Real Algebraic and Analytic Geometry |

Computation of the z-radical in C(X).

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homepage: http://personalpages.manchester.ac.uk/staff/Marcus.Tressl/index.php

Submission: 2004, November 24.

*Abstract:
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 IR^{n} 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.

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