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arXiv · 1510.07655

Sofic Mean Length

Hanfeng Li·Bingbing Liang
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Abstract

Given a length function L on the R-modules of a unital ring R, for each sofic group $Γ$ we define a mean length for every locally L-finite $RΓ$-module relative to a bigger $RΓ$-module. We establish an addition formula for the mean length. We give two applications. The first one shows that for any unital left Noetherian ring R, $RΓ$ is stably direct finite. The second one shows that for any $ZΓ$-module M, the mean topological dimension of the induced $Γ$-action on the Pontryagin dual of M coincides with the von Neumann-Lück rank of M.

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Hanfeng Li, Bingbing Liang. 2019-01-22. Sofic Mean Length. https://arxiv.org/abs/1510.07655

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