Definition:Associate/Integral Domain/Definition 2

Definition

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

Let $x, y \in D$.

$x$ and $y$ are associates (in $D$) if and only if:

$\ideal x = \ideal y$

where $\ideal x$ and $\ideal y$ denote the ideals generated by $x$ and $y$ respectively.

Also see

• Equivalence of Definitions of Associate in Integral Domain

• Results about associates can be found here.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62.3$ Factorization in an integral domain: $\text{(iii)}$