Prüfer Conditions in Rings with Zero- Divisors
نویسنده
چکیده
In his article: “Untersuchungen über die Teilbarkeitseigenschaften in Körpern” J. Reine Angew. Math. 168, 1 36, 1932 [21], Heinz Prüfer introduced a new class of integral domains, namely those domains R in which all finitely generated ideals are invertible. He also proved that to verify this condition, it suffices to check that it holds for all two-generated ideals of R. This was the modest beginning of the notion of a Prüfer domain, a notion which made, and continues to make, a significant impact on research in non-Noetherian commutative ring theory. Heinz Prüfer (1896 1934) in his short life, had no opportunity to see the rings named in his honor by Krull ([17], 1936). It is not an exaggeration to say that today there is no conference on a non Noetherian ring theory topic where the notion of a Prüfer domain does not make an appearance.
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