Publication detail

A note on involutoryautomorphisms of C and the use of algebrically independent numbers for the construction diagonable matrices

SKULA, L.

Czech title

Poznámka o involutorních automorfismech tělesa C a použití algebraicky nezávislých čísel ke konstrukci diagonálních matic

English title

A note on involutoryautomorphisms of C and the use of algebrically independent numbers for the construction diagonable matrices

Type

journal article - other

Language

en

Original abstract

The involutory aotomorphisms of the complex field are classified into three families" Archimedian – "like real numbers", Archimedian – "like a propper subfield of real numbers" and non-Archimedian. It is shown that these families have the same cardinality equal to exp exp aleph 0. By means of the involutory. automorphisms and Lindemann's criterion on algebraically independent numbers a class of diagonable matrices is constructed.

Czech abstract

Involutorní automorfismy tělesa komplexních čísel jsou rozděleny do tří tříd: obsahující archimedovské podtěleso reálných čísel, archimedovské vlastní podtěleso reálných čísel a obsahující nearchimedovské podtěleso. Kardinální číslo každé z těchto tříd je exp exp alef 0. Pomocí involutorních automorfismů tělesa komplexních čísel a Lindemannova kritéria o algebraicky nezávislých číslech je konstruhována třída diagonalizovatelných matic.

English abstract

The involutory aotomorphisms of the complex field are classified into three families" Archimedian – "like real numbers", Archimedian – "like a propper subfield of real numbers" and non-Archimedian. It is shown that these families have the same cardinality equal to exp exp aleph 0. By means of the involutory. automorphisms and Lindemann's criterion on algebraically independent numbers a class of diagonable matrices is constructed.

Keywords in Czech

Involutorní automorfismus tělesa komplexních čísel algebraicky nezávislé číslo; Lindemannovo kritérium; diagonalizovatelná matice.

Keywords in English

Involutory automorphism of the komplex field; algebraically independent number; Lindemann criterion; diagonable matrix.

RIV year

2005

Released

21.08.2005

Publisher

Universitatis Ostraviensis

Location

Ostrava

Journal

Acta Mathematica

Volume

2004

Number

12

Pages from–to

49–60

Pages count

12

BIBTEX


@article{BUT43161,
  author="Ladislav {Skula},
  title="A note on involutoryautomorphisms of C and the use of algebrically independent numbers for the construction diagonable matrices",
  journal="Acta Mathematica",
  year="2005",
  volume="2004",
  number="12",
  month="August",
  pages="49--60",
  publisher="Universitatis Ostraviensis",
  address="Ostrava"
}