Almost Quasi-Schreier Domains

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.