Electronic Resource
On the Krull dimension of rings of continuous semialgebraic functions
| العنوان: | On the Krull dimension of rings of continuous semialgebraic functions |
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| المؤلفون: | Fernando Galván, José Francisco, Gamboa, J. M. |
| بيانات النشر: | Universidad Autónoma Madrid 2023-06-19T14:57:54Z 2023-06-19T14:57:54Z 2015 |
| نوع الوثيقة: | Electronic Resource |
| مستخلص: | Let R be a real closed field, S(M) the ring of continuous semialgebraic functions on a semialgebraic set M subset of R-m and S* (M) its subring of continuous semialgebraic functions that are bounded with respect to R. In this work we introduce semialgebraic pseudo-compactifications of M and the semialgebraic depth of a prime ideal p of S(M) in order to provide an elementary proof of the finiteness of the Krull dimensions of the rings S(M) and S* (M) for an arbitrary semialgebraic set M. We are inspired by the classical way to compute the dimension of the ring of polynomial functions on a complex algebraic set without involving the sophisticated machinery of real spectra. We show dim(S(M)) = dim(S* (M)) = dim(M) and prove that in both cases the height of a maximal ideal corresponding to a point p is an element of M coincides with the local dimension of M at p. In case p is a prime z-ideal of S(M), its semialgebraic depth coincides with the transcendence degree of the real closed field qf(S(M)/p) over R GAAR Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub |
| مصطلحات الفهرس: | 512.7, Semialgebraic function, bounded semialgebraic function, z-ideal, semialgebraic depth, Krull dimension, local dimension, transcendence degree, real closed ring, real closed field, real closure of a ring, Geometria algebraica, 1201.01 Geometría Algebraica, journal article |
| URL: | MTM2011-22435 |
| الاتاحة: | Open access content. Open access content open access |
| ملاحظة: | application/pdf 0213-2230 English |
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| رقم الانضمام: | edsoai.on1413949699 |
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