The n‐order of algebraic triangulated categories

We quantify certain features of algebraic triangulated categories using the ‘n‐order’, an invariant that measures how strongly n annihilates objects of the form Y/n. We show that the n‐order of an algebraic triangulated category is infinite, and that the p‐order of the p‐local stable homotopy category is exactly p−1 for any prime p. In particular, the p‐local stable homotopy category is not algebraic.