Open Access
Translator Disclaimer
December 2015 Classification of Continuous Fractional Binary Operations on the Real and Complex Fields
Yuji KOBAYASHI, Sin-Ei TAKAHASI, Makoto TSUKADA
Tokyo J. Math. 38(2): 369-380 (December 2015). DOI: 10.3836/tjm/1452806046

Abstract

In this paper, we consider a classification problem for continuous fractional binary operations on $\mathbf K$, where $\mathbf K$ denotes the real field $\mathbf R$ or the complex field $\mathbf C$. We first show that there exist exactly two continuous fractional binary operations on $\mathbf R$ up to isomorphism. In the complex case, we describe completely all continuous fractional binary operations on $\mathbf C$ in terms of ordinary fraction. Applying this description, we give a partial solution to the classification problem in the complex case. Moreover we show that there exist exactly two homogeneous cancellative binary operations on $\mathbf K$ up to isomorphism.

Citation

Download Citation

Yuji KOBAYASHI. Sin-Ei TAKAHASI. Makoto TSUKADA. "Classification of Continuous Fractional Binary Operations on the Real and Complex Fields." Tokyo J. Math. 38 (2) 369 - 380, December 2015. https://doi.org/10.3836/tjm/1452806046

Information

Published: December 2015
First available in Project Euclid: 14 January 2016

zbMATH: 1364.30005
MathSciNet: MR3448863
Digital Object Identifier: 10.3836/tjm/1452806046

Subjects:
Primary: 30C40 , 42A38
Secondary: ‎32A36‎ , 46E22

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.38 • No. 2 • December 2015
Back to Top