algebraically's Usage Examples:

In mathematics, a field F is algebraically closed if every non-constant polynomial in F[x] (the univariate polynomial ring with coefficients in F) has.

algebra, a subset S {\displaystyle S} of a field L {\displaystyle L} is algebraically independent over a subfield K {\displaystyle K} if the elements of S.

algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

Moreover, it shows that quintic equations are, in general, algebraically unsolvable.

Over an algebraically closed field, a toral subalgebra is automatically abelian.

Thus, over an algebraically closed field of characteristic.

constructible points, which can again be described either geometrically or algebraically.

cardinality of an algebraically independent subset of L over K.

A subset S of L is a transcendence basis of L /K if it is algebraically independent over.

algebraic geometry, an affine variety, or affine algebraic variety, over an algebraically closed field k is the zero-locus in the affine space kn of some finite.

Over an algebraically closed field such as the complex numbers, all semisimple Lie algebras.

The set of Puiseux series over an algebraically closed field of characteristic 0 is itself an algebraically closed field, called the field of Puiseux.

An affine variety over an algebraically closed field is conceptually the easiest type of variety to define,.

In mathematics, a field F is called quasi-algebraically closed (or C1) if every non-constant homogeneous polynomial P over F has a non-trivial zero provided.

It relates algebraic sets to ideals in polynomial rings over algebraically closed fields.

Many results for diagonalizable matrices hold only over an algebraically closed field (such as the complex numbers).

Or to put it algebraically, given a prime number p n {\displaystyle p_{n}} , where n is its index.

For an algebraically closed field k, much of the structure of an algebraic variety X over.

tensor that has type I (at some event) is called algebraically general; otherwise, it is called algebraically special (at that event).

square of n to four times the (n - 1)th pronic number, or to put it algebraically, D n = n 2 + 4 ( n 2 − n ) {\displaystyle D_{n}=n^{2}+4(n^{2}-n)} .

To put it algebraically, the n-th octagonal number is x n = n 2 + 4 ∑ k = 1 n − 1 k = 3 n 2.