✦ LIBER ✦

Integral Non-commutative Spaces

✍ Scribed by S. Paul Smith

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 163 KB
Volume: 246
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8957

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✦ Synopsis

A non-commutative space X is a Grothendieck category Mod X. We say X is integral if there is an indecomposable injective X-module X such that its endomorphism ring is a division ring and every X-module is a subquotient of a direct sum of copies of 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 these notions behave as one might expect.

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