Rational criterion testing the density of additive subgroups of R^n and C^n

Authors

  • Mohamed Elghaoui University of Carthage
  • Adlene Ayadi University of Gafsa

DOI:

https://doi.org/10.4995/agt.2015.3257

Keywords:

dense, additive group, rationally independent, Kronecker.

Abstract

In this paper, we give an explicit criterion to decide the
density of finitely generated additive subgroups of R^n and C^n.

Downloads

Download data is not yet available.

Author Biographies

Mohamed Elghaoui, University of Carthage

Faculty of Sciences of Bizerte 7021 Jarzouna, Bizerte

Department of Mathematics

Adlene Ayadi, University of Gafsa

Faculty of sciences

References

A. Ayadi and H. Marzougui, Dense orbits for abelian subgroups of GL(n, $mathbb{C$), Foliations 2005, World Scientific, Hackensack, NJ, (2006), 47-69.

A. Ayadi, H. Marzougui and E. Salhi, Hypercyclic abelian subgroups of GL(n, $mathbb{R)$, J. Difference Equ. Appl. 18 (2012), 721-738.

http://dx.doi.org/10.1080/10236198.2011.582466

A. Ayadi, Hypercyclic abelian groups of affine maps on $mathbb{C}^{n}$, Canad. Math. Bull. 56 (2013), 477-490.

http://dx.doi.org/10.4153/CMB-2012-019-6

N. S. Feldman, Hypercyclic tuples of operators and somewhere dense orbits, J. Math. Anal. Appl. 346 (2008), 82-98.

http://dx.doi.org/10.1016/j.jmaa.2008.04.027

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Fourth Edition, Clarendon Press, Oxford, 1960.

L. Kronecker, Nherungsweise ganzzahlige Auflsung linearer Gleichungen, Monatsberichte Knigl. Preu. Akad. Wiss. Berlin, (1884), 1179-1193 and 1271-1299.

M. Waldschmidt,Topologie des points rationnels, Cours de troisi`eme Cycle, Universit'e P. et M. Curie (Paris VI), (1994/95).

Downloads

Published

2015-10-01

How to Cite

[1]
M. Elghaoui and A. Ayadi, “Rational criterion testing the density of additive subgroups of R^n and C^n”, Appl. Gen. Topol., vol. 16, no. 2, pp. 127–139, Oct. 2015.

Issue

Section

Articles