Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998
Association of Mizar Users
The Field of Quotients Over an Integral Domain

Christoph Schwarzweller

University of T\"ubingen
Summary.

We introduce the field of quotients over an integral domain
following the
wellknown construction using pairs over integral domains.
In addition we define ring homomorphisms and prove some basic facts about
fields of quotients including their universal property.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[4]
[14]
[15]
[12]
[2]
[3]
[9]
[10]
[13]
[7]
[6]
[1]
[8]
[5]

Preliminaries

Defining the Operations

Defining the Field of Quotients

Defining Ring Homomorphisms

Some Further Properties
Bibliography
 [1]
Czeslaw Bylinski.
Binary operations.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Jaroslaw Gryko.
On the monoid of endomorphisms of universal algebra and many sorted algebra.
Journal of Formalized Mathematics,
7, 1995.
 [6]
Eugeniusz Kusak, Wojciech Leonczuk, and Michal Muzalewski.
Abelian groups, fields and vector spaces.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Michal Muzalewski.
Construction of rings and left, right, and bimodules over a ring.
Journal of Formalized Mathematics,
2, 1990.
 [8]
Michal Muzalewski.
Categories of groups.
Journal of Formalized Mathematics,
3, 1991.
 [9]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Wojciech A. Trybulec.
Vectors in real linear space.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received May 4, 1998
[
Download a postscript version,
MML identifier index,
Mizar home page]