For simplicity we follow the rules: I, J denote sets, A, B denote many sorted sets of I, i, j, x are arbitrary, and S denotes a non empty many sorted signature. A set has common domain if: (Def.1) For all functions f , g such that f ∈ it and g ∈ it holds dom f = dom g. Let us mention that there exists a set which is functional and non empty and has common domain. The following proposition is tr...

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 …eld 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 ant...