# Lexicographical ordering and field operations in the complex plane

Author
Mathematical Institute, Slovak Academy of Sciences, Kosice
Abstract
Let $K \in \mathbb{N}, K \geq 3$. Let $\mathbb{C}_K = \mathbb{R}_0^K$ be the Cartesian product of $K$ copies of $\mathbb{R}_0$, where $\mathbb{R}_0$ denotes the set of all nonnegative real numbers. We equip this set with arithmetic operations and show that under the condition of the so-called Cancelation Law, the space $\mathbb{C}_K$ is arithmetically isomorphic with the standard field $\mathbb{C}$ of complex numbers. Distinct $K \in \mathbb{N}$ determine distinct lexicographical orderings on $\mathbb{C}$.
Keywords
lexicographical order; field operations; complex plane; isomorphism
Reference
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Pages
123-133
Volume
41
Issue
2
Year
2014
Journal
Matematychni Studii
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