Semistar GCD Domains

Abstract

We develop a theory of GCD domains with respect to a semistar operation. We present an axiomatic approach which covers various fundamental classes of GCD domains. This allows us to generalize and improve several classical properties of Bezout and GCD domains.

Key Words:

• Bezout domain
• GCD domain
• G-GCD domain
• PID
• Semistar operation

2000 Mathematics Subject Classification:

• Primary 13A15
• Secondary 13F05, 13G05

Notes

Communicated by I. Swanson.