# Search Results for ""

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**field**is any set of elements that satisfies the**field**axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a**field**is ...A prime

**field**is a finite**field**GF(p) for p is prime.A perfect

**field**is a**field**F such that every algebraic extension is separable. Any**field**in**field**characteristic zero, such as the rationals or the p-adics, or any finite ...A

**field**F in which any Pythagorean extension of F coincides with F.The ring of fractions of an integral domain. The

**field**of fractions of the ring of integers Z is the rational**field**Q, and the**field**of fractions of the polynomial ring ...A global

**field**is either a number**field**, a function**field**on an algebraic curve, or an extension of transcendence degree one over a finite**field**. From a modern point of view, ...If a

**field**has the property that, if the sets A_1, ..., A_n, ... belong to it, then so do the sets A_1+...+A_n+... and A_1...A_n..., then the**field**is called a Borel**field**...The

**field**of rationals is the set of rational numbers, which form a**field**. This**field**is commonly denoted Q (doublestruck Q).The

**field**of reals is the set of real numbers, which form a**field**. This**field**is commonly denoted R (doublestruck R).The characteristic exponent of a

**field**is 1 if the**field**characteristic is 0 and p if the**field**characteristic is p....