query: Why are There No "Triernions" (3-dimensional analogue of complex numbers / quaternions)?
positive_passages.docid: 26764
positive_passages.text: Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
negative_passages.docid: 22959
negative_passages.text: Does every even-dimensional sphere admit an almost complex structure?
negative_passages.docid: 46664
negative_passages.text: Is every endomorphism of the quaternion ring surjective?
negative_passages.docid: 137054
negative_passages.text: How to work with complex numbers in C?
negative_passages.docid: 80522
negative_passages.text: Quaternion rotation without Euler angles
negative_passages.docid: 83359
negative_passages.text: Complex number identity by trigonometry
negative_passages.docid: 106940
negative_passages.text: Why are complex numbers considered to be numbers?
negative_passages.docid: 155120
negative_passages.text: Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
negative_passages.docid: 112348
negative_passages.text: Defining the Complex numbers
negative_passages.docid: 134602
negative_passages.text: Convert quaternion to a different coordinate system
negative_passages.docid: 156245
negative_passages.text: What does it mean for the group of rotation matrices to have a "manifold structure"
negative_passages.docid: 42165
negative_passages.text: Complex numbers and Roots of unity
negative_passages.docid: 664
negative_passages.text: Minkowski's complex Euclidean space vs. the real pseudo-Euclidean version
negative_passages.docid: 35571
negative_passages.text: Euler Rotations in Ordinary Space
negative_passages.docid: 55065
negative_passages.text: Getting Values From Quaternions
negative_passages.docid: 53335
negative_passages.text: Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
negative_passages.docid: 51314
negative_passages.text: How to prove that a complex number is not a root of unity?