Surcomplex number

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A surcomplex number is a number of the form a+b\sqrt{-1}, where a and b are surreal numbers.[1][2] The surcomplex numbers form an algebraically closed field, isomorphic to the algebraic closure of the rational numbers extended by a proper class of algebraically independent transcendental elements. Up to field isomorphism, this fact characterizes the field of surcomplex numbers.[3]

[edit] References

  1. ^ Surreal vectors and the game of Cutblock, James Propp, August 22, 1994.
  2. ^ N. L. Alling, Foundations of analysis over surreal number fields, N. L. Alling, Amsterdam: North-Holland, 1987. ISBN 0-444-70226-1.
  3. ^ Theorem 27, On Numbers and Games, John H. Conway, 2nd ed., Natick, Massachusetts: A K Peters, Ltd., 2000. ISBN 1-56881-127-6.
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