primitive element

C2Finite Field Theory

(technical, academic)An element that generates the multiplicative group of a finite field, meaning every non-zero element of the field can be expressed as a power of this element.

Example

• In the field GF(7), 3 is a primitive element.

C2Algebraic Extensions

(technical, academic)An element in a field extension that can generate the entire extension field, allowing every element to be expressed as a polynomial in this element with coefficients from the base field.

Example

• The number √2 is a primitive element of the field extension ℚ(√2).

C2Lattice Theory

(technical, academic)An element that is not a positive integer multiple of any other element in the lattice.

Example

• In the lattice of integers, 1 is a primitive element.

C2Coalgebra

(technical, academic)An element on which the comultiplication maps to a specific value involving the element and the multiplicative identity.

C2Free Group

(technical, academic)An element that belongs to a free generating set of a given free group.

Example

• In the free group generated by {a, b}, both 'a' and 'b' are primitive elements.