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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.relationAlso published in: Journal of Algebra 539(2019), pp. 326-338. doi:10.1016/j.jalgebra.2019.08.014. https://doi.org/10.1016/j.jalgebra.2019.08.014
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.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
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
dc.identifier.urnurn:nbn:de:101:1-2019082215205839719139
dc.identifier.ppn1672112117


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