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 well-known 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.

MML Identifier: QUOFIELD

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]

Contents (PDF format)

  1. Preliminaries
  2. Defining the Operations
  3. Defining the Field of Quotients
  4. Defining Ring Homomorphisms
  5. 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 bi-modules 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]