Monomial

In algebra, a monomial is a polynomial that consists of only one member. A monomial is thus a product consisting of a coefficient and powers of a, rarely several variables.

Examples of monomials of the variable a:

Every polynomial is a sum of monomials of the same variable, for example, is

Composed of the following monomials:

Alternative definition

In parts of the literature (without coefficients ) is called monomial only the product of the variables. Following this speech, then the monomials have the following property:

If we consider the polynomial ring in variables over a field as a vector space over, then the set of monomials is a basis of this vector space.

In the special case of a single variable that base thus consists of the monomials