Article ID Journal Published Year Pages File Type
4597683 Journal of Pure and Applied Algebra 2007 11 Pages PDF
Abstract

In this paper, we prove a version of Freyd’s generating hypothesis for triangulated categories: if DD is a cocomplete triangulated category and S∈DS∈D is an object whose endomorphism ring is graded commutative and concentrated in degree zero, then SS generates (in the sense of Freyd) the thick subcategory determined by SS if and only if the endomorphism ring of SS is von Neumann regular. As a corollary, we obtain that the generating hypothesis is true in the derived category of a commutative ring RR if and only if RR is von Neumann regular. We also investigate alternative formulations of the generating hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the generating hypothesis is true.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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