Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

## Ternary Fields

Michal Muzalewski
Warsaw University, Bialystok
Wojciech Skaba
Nicolaus Copernicus University, Torun

### Summary.

This article contains part 3 of the set of papers concerning the theory of algebraic structures, based on the book [3, pp. 13-15] (pages 6-8 for English edition).\par First the basic structure $\langle F, 0, 1, T\rangle$ is defined, where $T$ is a ternary operation on $F$ (three argument operations have been introduced in the article [2]. Following it, the basic axioms of a ternary field are displayed, the mode is defined and its existence proved. The basic properties of a ternary field are also contemplated there.

Supported by RPBP.III-24.C6.

#### MML Identifier: ALGSTR_3

The terminology and notation used in this paper have been introduced in the following articles [6] [4] [5] [1] [2]

Contents (PDF format)

#### Bibliography

[1] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Michal Muzalewski and Wojciech Skaba. Three-argument operations and four-argument operations. Journal of Formalized Mathematics, 2, 1990.
[3] Wanda Szmielew. \em From Affine to Euclidean Geometry, volume 27. PWN -- D.Reidel Publ. Co., Warszawa -- Dordrecht, 1983.
[4] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[5] Wojciech A. Trybulec. Vectors in real linear space. Journal of Formalized Mathematics, 1, 1989.
[6] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.