Nonassociative Algebra
An Algebra which does not satisfy
is called a nonassociative algebra. Bott and Milnor (1958) proved that the only DivisionAlgebras are for
, 2, 4, and 8. Each gives rise to an Algebra with particularly usefulphysical applications (which, however, is not itself necessarily nonassociative), and these four cases correspond toReal Numbers, Complex Numbers, Quaternions, andCayley Numbers, respectively.See also Algebra, Cayley Number, Complex Number, Division Algebra, Quaternion,Real Number
References
Bott, R. and Milnor, J. ``On the Parallelizability of the Spheres.'' Bull. Amer. Math. Soc. 64, 87-89, 1958.
- Wilson's Theorem Corollary
- Wilson's Theorem (Gauss's Generalization)
- Winding Number (Contour)
- Winding Number (Map)
- Windmill
- Window Function
- Winkler Conditions
- Winograd Transform
- Wirtinger's Inequality
- Wirtinger-Sobolev Isoperimetric Constants
- Witch of Agnesi
- Witness
- Wittenbauer's Parallelogram
- Wittenbauer's Theorem
- Witten's Equations
- Wolstenholme's Theorem
- Woodall Number
- Woodbury Formula
- Word
- World Line
- Worm
- Worpitzky's Identity
- Writhe
- Wronskian
- Wulff Shape