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We survey and compare invariants of modules over the polynomial ring and the exterior algebra. In our considerations, we focus on the depth. The exterior analogue of depth was first introduced by Aramova, Avramov and Herzog. We state similarities between the two notion of depth and exhibit their relation in the case of squarefree modules. Work of Conca, Herzog and Hibi and Trung, respectively, shows that annihila-tor numbers are a meaningful generalization of depth over the polynomial ring. Wefatcat:scnfxrcjxbd2flwnh726ixtk4i