137 Citations
The use of infinity in pure number theory and algebra
- MathematicsInternational Journal of Algebra
- 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…
Residue class rings of real-analytic and entire functions
- Mathematics
- 2006
Let A(R) and E(R) denote respectively the ring of analytic and real entire functions in one variable. It is shown that if m is a maximal ideal of A(R), then A(R)/m is isomorphic either to the reals…
On the Teaching of Linear Algebra
- Education
- 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.…
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…
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…
A finite axiomatization of positive MV-algebras
- MathematicsAlgebra universalis
- 2022
. Positive MV-algebras are the subreducts of MV-algebras with re- spect to the signature {⊕ , ⊙ , ∨ , ∧ , 0 , 1 } . We provide a finite quasi-equational axiomatization for the class of such algebras.