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

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… Expand

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

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

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

. 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.