Algebraische Theorie der Körper.

  title={Algebraische Theorie der K{\"o}rper.},
  author={Ernst W. Steinitz},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={167 - 309}
  • E. Steinitz
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
The use of infinity in pure number theory and algebra
What is meant here by pure number theory is elementary number theory from Fermat to Kronecker, what I call Fermat-Kronecker arithmetic, that is the method of infinite descent combined with the theoryExpand
In memoriam Ernst Steinitz (1871–1928)
On ordered division rings
Part I. Embedding an ordered group in a division ring.
Rational maps $H$ for which $K(tH)$ has transcendence degree 2 over $K$
We classify all rational maps $H \in K(x)^n$ for which ${\rm trdeg}_K K(tH_1,tH_2,\ldots,tH_n) \le 2$, where $K$ is any field and $t$ is another indeterminate. Furthermore, we classify all such mapsExpand
On the Teaching of Linear Algebra
Foreword to the English Edition. Preface. Introduction. Part I: Epistemological Analysis of the Genesis of the Theory of Vector Spaces. 1. Introduction. 2. Analytical and Geometrical Origins. 3.Expand
Field Theory: From Equations to Axiomatization
7. THE ABSTRACT DEFINITION OF A FIELD. The developments we have been describing thus far lasted close to a century. They gave rise to important "concrete" theories-Galois theory, algebraic numberExpand
A general outline of the genesis of vector space theory
The following article presents a general outline of the genesis of the elementary concepts of vector space theory. It presents the main works that contributed to the development of these basicExpand
Steinitz Field Towers for Modular Fields
Derivations and automorphisms of locally matrix algebras and groups
ISSN 1025-6415. Допов. Нац. акад. наук Укр. 2020. No 9: 19—23 Ц и т у в а н н я: Bezushchak O.O. Derivations and automorphisms of locally matrix algebras and groups. Допов. Нац. акад. наук Укр. 2020.Expand
Hamming spaces and locally matrix algebras
We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces $( \mathbb{Z}/ 2 \mathbb{Z})^n $. We classify countable locally standard Hamming spaces and show thatExpand