division algebra
A "division algebra" is a mathematical structure where division by non-zero elements is always possible, often used in advanced fields like quantum physics and cryptography.
Definition
C2mathematics
(technical, academic)A mathematical structure where every non-zero element has a multiplicative inverse.
Example
- In a division algebra, you can always find an inverse for any non-zero element.
C2algebra
(technical, academic)A vector space over a field with a bilinear multiplication where every non-zero element has a unique inverse.
Example
- Quaternions are a well-known example of a division algebra.
C2number theory
(technical, academic)An algebraic structure where the set of non-zero elements forms a group under multiplication.
Example
- The real numbers form a division algebra because each non-zero number has an inverse.
Similar
Terms that have similar or relatively close meanings to "division algebra":
linear algebraassociative algebramatrix algebranon-associative algebrasquare divisionalgebraic structurealgebraic notationcommutative algebraalgebraic analysisalgebraic graph theory