Definition:Common Divisor/Integral Domain

Definition

Let $\struct {D, +, \times}$ be an integral domain.

Let $S \subseteq D$ be a finite subset of $D$.

Let $c \in D$ such that $c$ divides all the elements of $S$, that is:

$\forall x \in S: c \divides x$

Then $c$ is a common divisor of all the elements in $S$.

Also known as

A common divisor is also known as a common factor.

In Euclid's The Elements, the term common measure is universally used for this concept.

Also see

• Results about common divisors can be found here.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62$. Factorization in an integral domain