Content (algebra)
Encyclopedia
In algebra
, the content of a polynomial
is the highest common factor of its coefficients.
A polynomial is primitive
if it has content unity.
Gauss's lemma for polynomials
may be expressed as stating that for polynomials over a unique factorization domain
, the content of the product of two polynomials is the product of their contents.
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, the content of a polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
is the highest common factor of its coefficients.
A polynomial is primitive
Primitive polynomial
In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF...
if it has content unity.
Gauss's lemma for polynomials
Gauss's lemma (polynomial)
In algebra, in the theory of polynomials , Gauss's lemma is either of two related statements about polynomials with integer coefficients:...
may be expressed as stating that for polynomials over a unique factorization domain
Unique factorization domain
In mathematics, a unique factorization domain is, roughly speaking, a commutative ring in which every element, with special exceptions, can be uniquely written as a product of prime elements , analogous to the fundamental theorem of arithmetic for the integers...
, the content of the product of two polynomials is the product of their contents.