{wiki}

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: https://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


Ciro Santilli @cirosantilli 37

 Incoming links: Cross product