Algebraic Nilpotents
The two-dimensional dual numbers contain a nilpotent space. Other algebras and numbers that contain nilpotent spaces include split-quaternions (coquaternions), split-octonions, biquaternions, and complex octonions .
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“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
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