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

An algebraic variety over a field K that becomes isomorphic to a projective space.

The order of a finite field is the number of elements it contains.

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

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.

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

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.