Lexicographical ordering and field operations in the complex plane |
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Author |
gregor@saske.sk, jhaluska@saske.sk
Mathematical Institute, Slovak Academy of Sciences, Kosice
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Abstract |
Let K∈N,K≥3. Let CK=RK0 be the Cartesian product of K copies of R0, where R0 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 CK is arithmetically
isomorphic with the standard field C of complex numbers. Distinct K∈N determine distinct
lexicographical orderings on C.
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Keywords |
lexicographical order; field operations; complex plane; isomorphism
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Reference |
1. E. Haluskova, Two element direct limit classes of monounary algebras, Math. Slovaca, 52 (2002), 177–194.
2. V. Lenski, Generation of multi polarity electromagnetic energy, US patent from 15.11.2006, WO 2008/060342, PCT/US2007/01707. 3. N. Kutka, S. Goceikis, S. Adamovicius, Multipolarity radio telescope and radio transmission systems, Materials of the Multi polarity laboratory of cryptography, http://www.dkl.lt, Kaunas LT-50168, Jasalcio g.7, Lithuania. 4. E.M. Vechtomov, A.V. Cheraneva, Semifields and their properties, Jour. of Math. Sciences, 163 (2006), №6, translated from Fundamentalnaya i prikladnaya matematika, 14 (2008), №5, 3–54. (in Russian) 5. J.S. Golan, Some recent applications of semiring theory, Int. Conf. on Algebra in memory of Kostia Beidar, National Cheng Kung University, Taiwan, 2005, 18 p. |
Pages |
123-133
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Volume |
41
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Issue |
2
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Year |
2014
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Journal |
Matematychni Studii
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Full text of paper | |
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