Residue class rings of real-analytic and entire functions

• Autorzy: Marek Golasiński , Melvin Henriksen
• Języki publikacji: EN

Abstrakty

EN

Let 𝓐(ℝ) and 𝓔(ℝ) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if 𝔪 is a maximal ideal of 𝓐(ℝ), then 𝓐(ℝ)/𝔪 is isomorphic either to the reals or a real closed field that is an η₁-set, while if 𝔪 is a maximal ideal of 𝓔(ℝ), then 𝓔(ℝ)/𝔪 is isomorphic to one of the latter two fields or to the field of complex numbers. Moreover, we study the residue class rings of prime ideals of these rings and their Krull dimensions. Use is made of a classical characterization of algebraically closed fields due to E. Steinitz and techniques described in L. Gillman and M. Jerison's book on rings of continuous functions.

Kategorie tematyczne

• 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
• 30D20: Entire functions, general theory
• 26E05: Real-analytic functions
• 13B30: Rings of fractions and localization

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 104
• Numer: 1
• Strony: 85-97

Daty

wydano

2006

Twórcy

autor

Marek Golasiński

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Melvin Henriksen

• Department of Mathematics, Harvey Mudd College, Clarement, CA 91711, U.S.A.

Identyfikatory

DOI

10.4064/cm104-1-5