Definition:Associate/Integral Domain/Definition 2

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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

  • Results about associates can be found here.