Abstract
In this paper, we define the v -finiteness for a length function L v on the set of all v -ideals of an integral domain R and show that R is a Krull domain if and only if every proper integral v -ideal of R has v -finite length and L v ( ( A B ) v ) = L v ( A ) + L v ( B ) for every pair of proper integral v -ideals A and B in R . We also give Euclidean-like characterizations of factorial, Krull, and π -domains. Finally we define the notion of quasi- ∗ -invertibility and show that if every proper prime t -ideal of an integral domain R is quasi- t -invertible, then R is a Krull domain.
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