270 Field
A set of scalars with addition and multiplication that allow the usual arithmetic of numbers that is used to scale vectors in a vector space.
definition (Field) A type of ring with axioms (1) to (8) and the following additional condition:
- (Multiplicative Inverse) \(a \cdot a^{-1} = a^{-1} \cdot a = a\)
where
- \(a\) is a nonzero element of the field.
- \(a^{-1}\) is the multiplicative inverse of \(a\).
- \(\cdot\) is the multiplicative operation of the field.
Note:
- axioms (1) to (8) are the ring axioms.