Let Q[x] denote the ring of polynomials in an indeterminate x with coefficients in the field Q of rational numbers. An algebraic function field in one variable over Q is an extension of Q[x] of finite degree. For short, such fields will be called function fields. Note that function fields are to Q[x] what algebraic number fields are to Z. Since Q[x] is a natural ring (§1.2), divisor theory applies* to function fields.
KeywordsFunction Field Algebraic Curve Great Common Divisor Irreducible Polynomial Natural Ring
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