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The $$n$$-order of algebraic triangulated categories. (English) Zbl 1285.18018
Let $${\mathcal T}$$ be a triangulated category and let $$n$$ be a positive integer. The $$n$$-order of $${\mathcal T}$$ is an invariant whose value is a positive integer or infinity. It measures the strength of the relation $$n\cdot(Y/n)$$ for objects $$Y$$ in $${\mathcal T}$$, where $$Y/n$$ is the cone of multiplication by $$n$$ in $$Y$$. If $${\mathcal T}$$ is obtained from chain complexes in an additive category (that is, if $${\mathcal T}$$ is an algebraic triangulated category), then the $$n$$-order of $${\mathcal T}$$ is infinite for all $$n$$. But the $$p$$-local stable homotopy category for a prime number $$p$$ has $$p$$-order $$p-1$$ and is therefore not algebraic.

##### MSC:
 18E30 Derived categories, triangulated categories (MSC2010) 55P42 Stable homotopy theory, spectra
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