Document Type
Lecture
Publication Date
3-29-2006
Abstract
Let ��(ℂ), ��(ℝ), and ��(ℝ) denote, respectively, the ring of entire functions, the ring of real entire functions, and the ring of real analytic functions. In 1952, I showed that for any maximal ideal �� of ��(ℂ), then ��(ℂ)/�� is isomorphic to the complex field ℂ, even though it sometimes is infinite-dimensional as an algebra over ℂ. If �� is a maximal ideal of ��(ℝ), then ��(ℝ)/�� is either ℂ, ℝ, or a particular kind of non-Archimedean real-closed field containing ℝ. If �� is a maximal ideal of ��(ℝ), then ��(ℝ)/�� can be one of these three fields, but it is an open problem whether these are the only such fields.
Relational Format
presentation
Recommended Citation
Henriksen, Melvin, "Rings of Real Analytic and Real Entire Functions" (2006). Analysis Seminar. 47.
https://egrove.olemiss.edu/math_analysis/47
