Definition:Associate/Integral Domain/Definition 1
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Definition
Let $\struct {D, +, \circ}$ be an integral domain.
Let $x, y \in D$.
$x$ is an associate of $y$ (in $D$) if and only if they are both divisors of each other.
That is, $x$ and $y$ are associates (in $D$) if and only if $x \divides y$ and $y \divides x$.
Also see
Sources
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $6$: Polynomials and Euclidean Rings: $\S 26$. Divisibility
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 62$. Factorization in an integral domain: $(1)$