Polynomial ring/K/Greatest common divisor/Definition

Greatest common divisor

Let ${}P_{1},\ldots ,P_{n}\in K[X]$ denote polynomials over a field ${}K$. We say that a polynomial ${}G\in K[X]$ is a greatest common divisor of the given polynomials, if ${}G$ is a common divisor of the ${}P_{i}$, and if ${}G$ has among all common divisors of the ${}P_{i}$ maximal degree.