Abstract
Let X ⊂ An be an irreducible affine variety. Since its coordinate ring A(X) is an integral domain, we can form its quotient field; this is called the rational function field of X and is usually denoted K(X); its elements are called rational functions on X. Note that if Y ⊂ X is an open subset that is an affine variety in its own right (as in the discussion on page 19), the function field of Y will be the same as that of X.
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© 1992 Springer Science+Business Media New York
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Harris, J. (1992). Rational Functions and Rational Maps. In: Algebraic Geometry. Graduate Texts in Mathematics, vol 133. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2189-8_7
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DOI: https://doi.org/10.1007/978-1-4757-2189-8_7
Publisher Name: Springer, New York, NY
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