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dc.contributor.authorKropholler, Peter H.
dc.contributor.authorLorensen, Karl
dc.date.accessioned2019-08-16T06:31:21Z
dc.date.available2019-08-16T06:31:21Z
dc.date.issued2019-08-16
dc.identifier.urihttp://publications.mfo.de/handle/mfo/2513
dc.description.abstractA ring $R$ satisfies the $\textit{strong rank condition}$ (SRC) if, for every natural number $n$, the free $R$-submodules of $R^n$ all have rank $\leq n$. Let $G$ be a group and $R$ a ring strongly graded by $G$ such that the base ring $R_1$ is a domain. Using an argument originated by Laurent Bartholdi for studying cellular automata, we prove that $R$ satisfies SRC if and only if $R_1$ satisfies SRC and $G$ is amenable. The special case of this result for group rings allows us to prove a characterization of amenability involving the group von Neumann algebra that was conjectured by Wolfgang Lück. In addition, we include two applications to the study of group rings and their modules.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2019,22
dc.subjectGroup-graded ringen_US
dc.subjectStrong ranken_US
dc.subjectAmenable groupen_US
dc.titleGroup-Graded Rings Satisfying the Strong Rank Conditionen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2019-22
local.scientificprogramResearch in Pairs 2015en_US
local.series.idOWP-2019-22en_US
local.subject.msc16en_US
local.subject.msc20en_US
local.subject.msc43en_US


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