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We say that a Tychonoff space  X  has computable  z -radicals if for all idealsof  C ( X ), the smallest  z -ideal containingis generated as an ideal by all the  s  ○  f , where  f  is inand  s  is a continuous function ℝ → ℝ 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 ℝ  n   has computable  z -radicals if and only if  X  is locally closed.

Computation of the z -radical in C ( X )