The Ghost Dimension of a Ring
نویسندگان
چکیده
We introduce the concept of the ghost dimension gh. dim. R of a ring R. This is the longest nontrivial chain of maps in the derived category emanating from a perfect complex such that each map is zero on homology. We show that gh. dim. R ≤ w. dim. R, with equality if R is coherent or w. dim. R = 1.
منابع مشابه
The Ghost and Weak Dimensions of Rings and Ring Spectra
The primary object of this paper is to prove the conjecture of [HL08a] explaining how to recover the weak dimension of a ring from its derived category. In the process, we develop a theory of weak dimension, which we call ghost dimension, for the generalized rings, known as ring spectra, that arise in algebraic topology.
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