An infinite analogue of rings with stable rank one

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dc.creatorAra, Pere
dc.creatorPedersen, Gert K.
dc.creatorPerera, Francesc
dc.date1999-10-25
dc.date1999-10-26
dc.date.accessioned2026-07-07T05:31:16Z
dc.date.available2026-07-07T05:31:16Z
dc.descriptionReplacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings), and include examples like the ring of endomorphisms of a vector space over a field F, and the ring of all row- and column- finite matrices over F. We show that the category of QB-rings is stable under the formation of corners, ideals and quotients, as well as matrices and direct limits. We also give necessary and sufficient conditions for an extension of QB-rings to be again a QB-ring, and show that extensions of B-rings often lead to QB-rings. Specializing to the category of exchange rings we characterize the subset of exchange QB-rings as those in which every von Neumann regular element extends to a maximal regular element, i.e. a quasi-invertible element. Finally we show that the C*- algebras that are QB-rings are exactly the extremally rich C*-algebras previously studied by L.G. Brown and the second author.
dc.description41 pages
dc.identifierhttps://arxiv.org/abs/math/9910131
dc.identifierhttp://arxiv.org/abs/math/9910131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/79280
dc.subjectRings and Algebras
dc.subjectOperator Algebras
dc.subject16A12;16A30;16A32,46L05
dc.titleAn infinite analogue of rings with stable rank one
dc.typetext

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