Definition:Common Divisor/Integral Domain
< Definition:Common Divisor(Redirected from Definition:Common Divisor of Ring Elements)
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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