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Definition: Generalization of Divisor

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

We call $a$ a divisor of $b$ (denoted by $a\mid b$), if and only if there exists an element $c\in R$ such that $ac=b.$

Notes

  • This definition corresponds to the special case of a divisor, if $R=\mathbb Z.$

| | | | | created: 2019-06-27 18:36:41 | modified: 2019-06-27 21:25:56 | by: bookofproofs | references: [8250]


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Bibliography (further reading)

[8250] Koch, H.; Pieper, H.: “Zahlentheorie – Ausgewählte Methoden und Ergebnisse”, Studienbücherei, 1976

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