Nonassociative (Adjective)
Meaning
Not associative.
Classification
All adjective clusters.
Examples
- The binary operation of subtraction is nonassociative, since (a - b) - c is not equal to a - (b - c) in general.
- Lie algebras are nonassociative algebras used to describe the Lie groups which are fundamental in differential geometry and theoretical physics.
- The octonions and sedenions are nonassociative extension of quaternions and are used in alternative theories as to the structure of physical space-time.
- Jordan algebras are nonassociative algebras and are used mathematically rather than being the result of any analysis of the world.
- The nonassociative property of Riemann's vector sum significantly deviates from Euclid's original assumption.