JP Journal of Algebra, Number Theory and Applications
Volume 14, Issue 1, Pages 97 - 119
(June 2009)
|
|
THE SOURCE OF THE RATIONAL NUMBERS
AND RINGS OF FRACTIONS
Kazuyuki Hatada (Japan)
|
of
the rational numbers from the set of natural numbers
and
rings of fractions
from commutative rings A.
In it we do neither define the addition + and the multiplication × by
and
nor use polynomial rings containing
the rational integers
(resp. A).
We can prove these equations and also
They are not consequences of
definitions. We use local rings.