135 Citations
The use of infinity in pure number theory and algebra
- Mathematics
- 2019
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 theory… Expand
Rational maps $H$ for which $K(tH)$ has transcendence degree 2 over $K$
- Mathematics
- 2015
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 maps… Expand
On the Teaching of Linear Algebra
- Mathematics
- 2002
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
- Mathematics
- 1999
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 number… Expand
A general outline of the genesis of vector space theory
- 1995
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 basic… Expand
Derivations and automorphisms of locally matrix algebras and groups
- Mathematics
- 2020
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
- Mathematics
- 2020
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 that… Expand