 Algebra over a field

ID: algebra-over-a-field

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Algebra over a field by

Ciro Santilli 37 Updated 2025-07-16

A vector field with a bilinear map into itself, which we can also call a "vector product".

Note that the vector product does not have to be neither associative nor commutative.

Examples: en.wikipedia.org/w/index.php?title=Algebra_over_a_field&oldid=1035146107#Motivating_examples

complex numbers, i.e. $R^{2}$ with complex number multiplication
$R^{3}$ with the cross product
quaternions, i.e. $R^{4}$ with the quaternion multiplication

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