Mori Domains Whose Primary t-Ideals Are Valuation Ideals

Abstract

We show that if R is a Mori domain,then every height-one primary t-ideal is a valuation ideal if and only if ⋂ _{P∈X ¹(R)} R _P is a Krull domain where X ¹(R) is the set of height-one prime ideals of R. We give examples of non-Krull Mori-domains in which each height-one primary t-ideal is a valuation ideal.

Key Words:

• Mori domain
• Krull domain
• Valuation ideal
• Primary ideal

2000 AMS Subject Classification:

• 13A15
• 13A18
• 13B25
• 13E05
• 13G05

Acknowledgment

The second author's work was supported by Korea Research Foundation Grant(KRF-2001-DP0024).