半代数函数的中间代数

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-14 DOI:10.1016/j.topol.2025.109547

E. Baro, José F. Fernando, J.M. Gamboa

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引用次数: 0

摘要

我们将半代数集X上半代数函数S(X)环和有界半代数函数S(X)环之间的中间r -代数A刻画为S(X)的分数环。这使得我们可以计算A的Krull维数，A的剩余域在R上的超越度，并得到阿基米德R-代数A的Łojasiewicz不等式和Nullstellensatz。此外，我们还研究了由适当理想生成的中间R-代数，并证明了这种R-代数中函数的一个可拓定理。

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Intermediate algebras of semialgebraic functions

We characterize intermediate

R

-algebras A between the ring of semialgebraic functions

S (X)

and the ring

S^{⁎} (X)

of bounded semialgebraic functions on a semialgebraic set X as rings of fractions of

S (X)

. This allows us to compute the Krull dimension of A, the transcendence degree over

R

of the residue fields of A and to obtain a Łojasiewicz inequality and a Nullstellensatz for archimedean

R

-algebras A. In addition we study intermediate

R

-algebras generated by proper ideals and we prove an extension theorem for functions in such

R

-algebras.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.