Abstract
As an extension of the (pre)-Schreier domains studied by Cohn, McAdam, Rush, and Zafrullah, we study the class of integral domains D characterized by the property that whenever I ⊇ J
1
J
2 with I, J
1, J
2 invertible ideals of D, there exist an integer k ≥ 1 and ideals I
1, I
2 such that I
k
= I
1
I
2, ,
. The quasi-Schreier domains and the almost-Schreier domains, recently introduced by the second author, Moldovan and Khalid, satisfy this property.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The first author was partially supported by an HEC (Higher Education Commission, Pakistan) grant. The second author gratefully acknowledges the warm hospitality of the Abdus Salam School of Mathematical Sciences GCU Lahore during his visits in 2006–2010.
Notes
Communicated by I. Swanson.