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Split

To split over a field K, a polynomial p(x)=sumc_ix^i must satisfy

p(x)=aproduct_(i)(x-alpha_i)

where a and alpha_i are in K. Then the polynomial is said to split into linear factors. For example, x^2+1 splits over the field of complex numbers since x^2+1=(x-i)(x+i).

See also

Field, Split Exact Sequence, Splitting Field

This entry contributed by Todd Rowland

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References

Jacobson, N. Algebra. New York: W. H. Freeman, p. 224, 1985.

Referenced on Wolfram|Alpha

Split

Cite this as:

Weisstein, Eric W., with contributions by Todd Rowland. "Split." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Split.html

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