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Def. S. 13Ein Ring ist eine Menge R mit zwei assoziativen Verknüpfungen+: R × R → R und ·: R × R → R,so dass die folgenden Eigenschaften erfüllt sind.- R mit + ist eine abelsche Gruppe.- Für alle a, b, c ∈ R gilt das Distributivgesetz:a · (b + c) = a · b + a · c sowie (b + c) · a = b · a + c · a.In einem Ring heisst ein Element 1 ∈ R Einselement falls gilt:- 1 · a = a = a · 1 für alle a ∈ R.Ein Ring heisst kommutativ falls zusätzlich gilt:- a · b = b · a für alle a, b ∈ R.
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