In mathematics, a Goldman domain or G-domain is an integral domain A whose field of fractions is a finitely generated algebra over A.
An overring (i.e., an intermediate ring lying between the ring and its field of fractions) of a Goldman domain is again a Goldman domain.
There exists a Goldman domain where all nonzero prime ideals are maximal although there are infinitely many prime ideals.
A Goldman ideal is thus prime, but not necessarily maximal.
Since a factor ring is an integral domain if and only if the ring is factored by a prime ideal, every G-ideal is also a prime ideal.
[4] Every maximal ideal is a G-ideal, since quotient by maximal ideal is a field, and a field is trivially a G-domain.
[6] A Noetherian domain is a G-domain if and only if its Krull dimension is at most one, and has only finitely many maximal ideals (or equivalently, prime ideals).