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by Ciro Santilli (@cirosantilli, 25)
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Algebra over a field

 wiki
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A vector field with a bilinear map into itself, which we can also call a "vector product".
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Note that the vector product does not have to be neither associative nor commutative.
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Examples: en.wikipedia.org/w/index.php?title=Algebra_over_a_field&oldid=1035146107#Motivating_examples
  • complex numbers, i.e. R2 with complex number multiplication
  • R3 with the cross product
  • quaternions, i.e. R4 with the quaternion multiplication
  •  Table of contents
    • Division algebra link
      • Frobenius theorem link Division algebra
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Division algebra

 Algebra over a field toc wiki
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An algebra over a field where division exists.
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Frobenius theorem (real division algebras)

 Division algebra toc wiki tags: Classification
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There are 3: real numbers, complex numbers and quaternions.
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Notably, the octonions are not associative.

 Ancestors

  1. Vector field
  2. Field
  3. Ring
  4. Group
  5. Algebra
  6. Area of mathematics
  7. Mathematics
  8. Index

 Incoming links

  • Algebra
  • Baker-Campbell-Hausdorff formula
  • Complex number
  • Division algebra
  • Infinitesimal generator
  • Lie algebra

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