Monoid Domain Constructions of Antimatter Domains

Abstract

An integral domain without irreducible elements is called an antimatter domain. We give some monoid domain constructions of antimatter domains. Among other things, we show that if D is a GCD domain with quotient field K that is algebraically closed, real closed, or perfect of characteristic p > 0, then the monoid domain D[X; ℚ⁺] is an antimatter GCD domain. We also show that a GCD domain D is antimatter if and only if P⁻¹ = D for each maximal t-ideal P of D.

Key Words:

• Antimatter domain
• Atom
• GCD domain
• Monoid domain
• Schreier domain

AMS Subject Classification:

• 13A05
• 13F99

Notes

Communicated by A. Facchini.