Quote:
Originally Posted by Topologist
Here's a specific case where that makes a difference. I often work with systems that are anticommutative, meaning that there's a multiplication with yx = xy. Looking at the case where y = x, that means that x^{2} = x^{2}. That's fine and always true mod 2, but mod an odd prime it means that we have to have x^{2} = 0. The latter puts a significant restriction on what anticommutative structures are possible mod an odd prime that isn't present working mod 2.

Interesting. I'm familiar with Clifford algebras, specifically geometric and spacetime algebra, which are simply the threedimensional Clifford algebra and the fourdimensional Clifford algebra with the Minkowski metric, respectively. In those algebras, vector multiplication is anticommutative but x^{2} for x some vector of grade 1 or higher isn't 0, it's simply the dot product; if x is a basis vector, it's either 1 or 1, depending on the metric.
The only place I already knew about where x^{2} = 0 is in a form of nonstandard analysis where d^{2} = 0, such that differentiation can be done algebraically.
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