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Peirce's Theorem


The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of complex numbers, and the algebra of quaternions with real coefficients.


See also

Complex Number, Quaternion, Real Number, Weierstrass's Theorem

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References

Schafer, R. D. "The Peirce Decomposition." §3.2 in An Introduction to Nonassociative Algebras. New York: Dover, pp. 32-37, 1996.

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Peirce's Theorem

Cite this as:

Weisstein, Eric W. "Peirce's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PeircesTheorem.html

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