Fernando Galván, José Francisco2023-06-192023-06-1920140033-560610.1093/qmath/hat048https://hdl.handle.net/20.500.14352/33760In 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 subset of R-m. 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/65/3/893.abstractrestricted access512.7Semialgebraic functionZariski spectrumMaximal spectrumReal closed ringsemialgebraic compacticationChain of prime idealsMaximal idealMinimal prime idealZ-idealSemialgebraic depthFamily of bricksLocal compactnessGeometria algebraica1201.01 Geometría Algebraica