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A variable that may assume only real values.

A field F in which any Pythagorean extension of F coincides with F.

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 following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

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

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

A vector field v for which the curl vanishes, del xv=0.

The characteristic exponent of a field is 1 if the field characteristic is 0 and p if the field characteristic is p.

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...