%0 Journal Article
%A Fernando Galván, José Francisco
%T On chains of prime ideals in rings of semialgebraic functions
%D 2014
%@ 0033-5606
%U https://hdl.handle.net/20.500.14352/33884
%X In this work, we study the structure of non-refinable chains of prime ideals in the (real closed) rings s(M) and s*(M) of semialgebraic and bounded semialgebraic functions on a semialgebraic set M⊂ℝm. We pay special attention to the prime z-ideals of s(M) and the minimal prime ideals of both rings. For the last, a decomposition of each semialgebraic set as an irredundant finite union of closed pure dimensional semialgebraic subsets plays a crucial role. We prove moreover the existence of maximal ideals in the ring s(M) of prefixed height whenever M is non-compact.
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