OurBigBook.com $£ Sponsor 中国独裁统治 China Dictatorship 新疆改造中心、六四事件、法轮功、郝海东、709大抓捕、2015巴拿马文件邓家贵、低端人口、西藏骚乱

Algebra over a field

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

Table of contents 55 2
- Division algebra Algebra over a field 14 1
  - Frobenius theorem (real division algebras, Classification of associative real division algebras) Division algebra 11

 Ancestors (8)

 Incoming links (6)