Lexicographical ordering and field operations in the complex plane
Tomáš Gregor, Ján Haluška · Matematychni Studii · 2014
Let K ∈ N, K ≥ 3. Let C K = R K 0 be the Cartesian product of K copies of R 0 , where 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 C K is arithmetically isomorphic with the standard field C of complex numbers.Distinct K ∈ N determine distinct lexicographical orderings on C. Т. Грегор, Я. Галушка.Лексикографический порядок и операции поля на комплексной площади // Мат.Студiї.