RESCINDED: Quaternion Series as a Division Algebra
Channel: Doug Sweetser
Date: 2018-09-09

Quaternion series are NOT a division algebra. Instead, quaternion series ARE a semigroup with inverses. I was aware these is more than one inverse for multiplication. That makes it a semigroup. 

Original description:

A white board talk is presented to first define what a quaternion series is - a totally ordered array of quaternions with a row and column values defined such that rows * columns = the length of the array. To be a division algebra, both addition and multiplication must be group operations. That in turn involves showing four things: identity, inverse, closure, and associativity.

[There are 2^n inverses, not one, which makes this a semigroup, not a division algebra.]

A Jupyter notebook to accompany this notebook is available here: https://github.com/dougsweetser/QM/blob/master/docs/quaternion_series_division_algebra.ipynb