ABSTRACT
In this paper, we define 
-factorable and unique -factorable domains for any star operation and show that (1) an integral domain R is a PID (resp., Dedekind domain, DVR) if and only if it is a factorable Bézout (resp., Prüfer, valuation) domain, (2) R is a UFD (resp., -domain, Krull domain) if and only if it is a t-factorable GCD-domain (resp., G-GCD domain, PVMD), and (3) R is a Krull domain if and only if it is a unique t-factorable domain.
ACKNOWLEDGMENTS
We would like to thank the referee for several helpful suggestions. The third author was supported in part by funds from the Basic Science Research Institute Program, Korea Research Foundation, 1998-015-D00017.
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