Fernando Galván, José Francisco2023-06-192023-06-1920140033-560610.1093/qmath/hat048https://hdl.handle.net/20.500.14352/33884In 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.engjournal articlehttp://qjmath.oxfordjournals.org/content/65/3/893restricted access512Álgebra1201 Álgebra