Adjunction of the associated sheaf functor of non-commutative rings

Shu-Hao Sun

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Abstract

We first extend the notion of structure sheaf for left noetherian rings in the sense of Van Oystaéyen to non-noetherian case; and then, by choosing a suitable sheaf category whose restriction to commutative rings yields the classical one, we prove that, for a vast class of non-necessarily commutative rings (including all commutative rings, all left stable left noetherian rings and all biregular rings) the structure sheaf functor admits a right adjoint, and is therefore exact. 

Original languageEnglish
Pages (from-to)195-206
Number of pages12
JournalJournal of Pure and Applied Algebra
Volume102
Issue number2
DOIs
Publication statusPublished - 28 Jul 1995
Externally publishedYes

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