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Function field (scheme theory)

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In mathematics the function field of an irreducible algebraic variety is the field of fractions of the ring of regular functions.

The ring of regular functions is an integral domain if and only if the variety is irreducible, and in this case the field of fractions is defined. It is a field extension of the ground field over which the variety is defined. The transcendence degree is called the dimension of the variety.

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