Groups {field, mathematics} can have two operations, such as adding and multiplying. For example, rational numbers and real numbers form mathematical fields over addition and multiplication. The rational-function field (which includes polynomials) has adding and multiplying operations. Rational numbers, real numbers, and rational functions are infinite fields. Other fields are algebraic number fields (algebras), relative Galoisian fields (Galoisian equation), relative Abelian fields (polynomial equations), class fields, valuation fields, separable fields, and prime fields.
Fields {p-adic number} {p-adic field} can have sums, from -p to infinity, of rational number times prime numbers.
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Date Modified: 2022.0225