Associates

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The associates of a number in a ring are the products of that number by each of the units. For example, among the Gaussian integers, the associates of $3+2i$ are $-3-2i$, $-2+3i$ and $2-3i$, which are the original number multiplied by –1, $i$ and $-i$ respectively. A number is one of its own associates, as it is itself multiplied by 1.

It is common to mod out associates, identifying (for example) –3 and 3 as members of the same equivalence class.