Integral Non-commutative Spaces

Abstract

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.