Definition: Unit

Let $(R,\cdot,+)$ be an integral domain with the multiplicative neutral element $1.$ And element $a\in R$ is called a unit of $R,$ if $$a\mid 1\,$$ i.e. $a$ is a divisor of $1$.

Notes

Examples

  1. Proposition: Group of Units

Definitions: 1 2 3
Proofs: 4 5 6 7 8 9
Propositions: 10 11


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References

Bibliography

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