Integral non-commutative spaces

[摘要] A non-commutative space X is a Grothendieck category ModX. We say X is integral if there is an indecomposable injective X-module E-x such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of E-x. A noetherian scheme is integral in this sense if and only if it is integral in the usual sense. We show that several classes of non-commutative spaces are integral. We also define the function field and generic point of an integral space and show that those notions behave as one might expect. (C) 2001 Elsevier Science.

[发布日期] 2001-12-15