Category:Definitions/Gaussian Rationals

From ProofWiki
Jump to navigation Jump to search

This category contains definitions related to Gaussian Rationals.
Related results can be found in Category:Gaussian Rationals.

Definition 1

A Gaussian rational is a complex number whose real and imaginary parts are both rational numbers.

That is, a Gaussian rational is a number in the form:

$a + b i: a, b \in \Q$

Definition 2

The field $\sqbrk {\Q \sqbrk i, +, \times}$ of Gaussian rationals is the field of quotients of the integral domain $\struct {\Z \sqbrk i, +, \times}$ of Gaussian integers.

This is shown to exist in Existence of Field of Quotients.

In view of Field of Quotients is Unique, we construct the field of quotients of $\Z \sqbrk i$, give it a label $\Q \sqbrk i$ and call its elements Gaussian rationals.

Pages in category "Definitions/Gaussian Rationals"

The following 4 pages are in this category, out of 4 total.