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Prop. 1.14Sei R ein euklidischer Ring und a ∈ R eine von Null verschiedene Nichteinheit. Dann sind folgende Aussagen äquivalent:(i) Für alle b ∈ R gilt: Ist a kein Teiler von b, so gibt es ein c ∈ R, so dass a Teiler von bc - 1 ist.(ii) Für alle b, b' ∈ R gilt: Ist a Teiler von bb', so ist a Teiler von b oder von b'.(iii) Für alle b, b' ∈ R gilt: Ist a = bb', so ist b oder b' eine Einheit.

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