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A theorem which treats constructions of fields of field characteristic p.

A field K is said to be algebraically closed if every polynomial with coefficients in K has a root in K.

An extension A subset B of a group, ring, module, field, etc., such that A!=B.

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.

Chevalley's theorem, also known as the Chevalley-Waring theorem, states that if f is a polynomial in F[x_1,...,x_n], where F is a finite field of field characteristic p, and ...

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.

The curl of a vector field, denoted curl(F) or del xF (the notation used in this work), is defined as the vector field having magnitude equal to the maximum "circulation" at ...

A linear transformation x_1^' = a_(11)x_1+a_(12)x_2+a_(13)x_3 (1) x_2^' = a_(21)x_1+a_(22)x_2+a_(23)x_3 (2) x_3^' = a_(31)x_1+a_(32)x_2+a_(33)x_3, (3) is said to be an ...