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The doublestruck letter R denotes the field of real numbers.

A vector field on a circle in which the directions of the vectors are all at the same angle to the circle.

Let F be a field of field characteristic p. Then the Frobenius automorphism on F is the map phi:F->F which maps alpha to alpha^p for each element alpha of F.

The topological completion C of a field F with respect to the absolute value |·| is the smallest field containing F for which all Cauchy sequences or rationals converge.

A cubic curve is an algebraic curve of curve order 3. An algebraic curve over a field K is an equation f(X,Y)=0, where f(X,Y) is a polynomial in X and Y with coefficients in ...

Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...

An extension of an arbitrary field F of the form F(sqrt(1+lambda^2)), where lambda in F.

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

Perhaps the most commonly-studied oriented point lattice is the so-called north-east lattice which orients each edge of L in the direction of increasing coordinate-value. ...