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The nth roots of unity are roots e^(2piik/n) of the cyclotomic equation x^n=1, which are known as the de Moivre numbers. The notations zeta_k, epsilon_k, and epsilon_k, where ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

A real quantity having a value less than zero (<0) is said to be negative. Negative numbers are denoted with a minus sign preceding the corresponding positive number, i.e., ...

The roots of a semisimple Lie algebra g are the Lie algebra weights occurring in its adjoint representation. The set of roots form the root system, and are completely ...

A separable algebraic extension E of F for which every irreducible polynomial in F which has a single root in E has all its roots in E is said to be Galoisian. Galoisian ...

The root lattice of a semisimple Lie algebra is the discrete lattice generated by the Lie algebra roots in h^*, the dual vector space to the Cartan subalgebra.

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

A radical integer is a number obtained by closing the integers under addition, multiplication, subtraction, and root extraction. An example of such a number is RadicalBox[7, ...

In set theory, a unary operation on set A is a function A->A. More generally, a unary operation is a function with exactly one operand, such as the factorial, square root, or ...

An algebraically soluble equation of odd prime degree which is irreducible in the natural field possesses either 1. Only a single real root, or 2. All real roots.