Hypercomplex Numbers of Dimension 10

Authors: Valery Timin

This work is devoted to the search, study and compilation of the multiplication table of a compound hyperbolic (Hypercomplex) number of dimension nine (10): q = {1, i1, i2, i3, …, i9, }: in2 = 1. On this basis, as a template, you can choose other multiplication tables with a different target or arbitrary arrangement of plus (+) and minus (-) characters in the cells of the multiplication table. The disadvantage of multiplication tables of dimension 10 is that they are neither associative nor commutative (not even anticommutative). But this is their fundamental property.. Эта работа посвящена поиску, изучению и составлению таблицы умножения составного гиперболического (гиперкомплексного) числа размерностью девять (10): q = {1, i1, i2, i3, …, i9, }: in2 = 1. На этой основе как на шаблоне можно подобрать другие таблицы умножения с другой целевой или произвольной расстановкой знаков "плюс" (+) и "минус" (-) в ячейках таблицы умножения. Только коммутативных таблиц размерности 10 может быть до 1750, а ассоциативных – до 65201 (не окончательно). Все коммутативные таблицы имеют эластичную ассоциативность (Am).

Comments:, 4 pages in Russian

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Submission history

[v1] 2019-10-05 09:50:32

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