"M-algebra" and "hypernumber Levels"
Musès was convinced that the basic laws of arithmetic on the reals are in direct correspondence with a concept where numbers could be arranged in "levels", where fewer arithmetical laws would be applicable with increasing level number. However, this concept was not developed much further beyond the initial idea, and defining relations for most of these levels have not been constructed.
Higher dimensional numbers built on the first three levels were called "M-algebra" by Musès if they yielded a distributive multiplication, unit element, and multiplicative norm. It contains kinds of octonions and historical quaternions (except A. MacFarlane's hyperbolic quaternions) as subalgebras. A proof of completeness of M-algebra has not been provided.
Read more about this topic: Musean Hypernumber
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