Integral Basis

An integral basis of a number field is a basis of its ring of integers as a free module over . Its length equals the extension field degree . For , the elements 1 and give an integral basis (Milne 2020, pp. 35-36 and 39).

An integral basis of the number field generated by an algebraic number is computed in the Wolfram Language as NumberFieldIntegralBasis[a].

See also

Basis, Number Field, Number Field Discriminant, Ring of Integers

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References

Milne, J. S. "Algebraic Number Theory." 19 Jul 2020. https://www.jmilne.org/math/CourseNotes/ANT.pdf.

Cite this as:

Weisstein, Eric W. "Integral Basis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IntegralBasis.html

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