Monoid domain constructions of antimatter domains

摘要

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 DX ;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.