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.
Notes
Communicated by A. Facchini.