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.

Key Words:

• Class group
• Integrally closed domain
• Schreier domain

2010 Mathematics Subject Classification:

• Primary 13A15
• Secondary 13F05

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.