Abstract
Let D be an integral domain and S ≠ U(D) a saturated multiplicative subset of D. We say that S is a GCD-set (resp., factorial-set) if S is a GCD-monoid (resp., factorial-monoid) under the product of D and that S is a Marot-set if every integral ideal of D intersecting S is generated by a set of elements in S. In this paper, we study Marot GCD-sets and Marot factorial-sets.
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Acknowledgments
We would like to thank the referee for several helpful suggestions. The second author's work was supported grant No. R02-2000-00016 from the Basic Science Research Program of the Korea Science & Engineering Foundation.
Notes
#Communicated by S. Wiegand.