  This paper introduces a notion of integrality that is suitable for
non-commutative varieties. It is compatible with the usual notion of
integrality for schemes. The function field and generic point of a
non-commutative integral space are also defined. These agree with the usual
notion for noetherian schemes. It is shown that these notions behave as one
would wish. For example, various non-commutative analogues of projective space
are integral.
