Definition: Associate

Let $(R,\cdot,+)$ be an integral domain with the multiplicative neutral element $1,$ and let $a,b\in R.$

We call $a$ an associate of $b$ (denoted by $a\sim b$) if and only if: $$a\mid b\wedge b\mid a,$$ i.e. $a$ is a divisor of $b$ and vice versa.

Notes

  1. Lemma: A Criterion for Associates

Definitions: 1
Lemmas: 2
Proofs: 3 4 5
Propositions: 6


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References

Bibliography

  1. Koch, H.; Pieper, H.: "Zahlentheorie - Ausgewählte Methoden und Ergebnisse", Studienbücherei, 1976