THE REALIZATION PROBLEM FOR VON NEUMANN REGULAR RINGS

DOI10.1142/9789812818331_0004zbMath1183.16011arXiv0802.1872OpenAlexW2036179438MaRDI QIDQ3633652

Pere Ara

Publication date: 23 June 2009

Published in: Ring Theory 2007 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.1872

zbMATH Keywords

von Neumann regular ringsLeavitt path algebrasseparative cancellationrefinement monoids

Mathematics Subject Classification ID

Commutative semigroups (20M14) Grothendieck groups, (K)-theory, etc. (16E20) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

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Simplicial and dimension groups with group action and their realization ⋮ AF inverse monoids and the structure of countable MV-algebras ⋮ Primely generated refinement monoids ⋮ \(\mathbf K_0\) of semiartinian von Neumann regular rings. Direct finiteness versus unit-regularity ⋮ The Realization Problem for some wild monoids and the Atiyah Problem ⋮ The realization problem for finitely generated refinement monoids ⋮ Tame and wild refinement monoids ⋮ Adjoining a universal inner inverse to a ring element. ⋮ Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions ⋮ The regular algebra of a poset ⋮ Representing finitely generated refinement monoids as graph monoids ⋮ Representation of Artinian partially ordered sets over semiartinian von Neuman regular algebras. ⋮ Leavitt path algebras over a poset of fields ⋮ Refinement monoids and adaptable separated graphs ⋮ Leavitt path algebras: the first decade ⋮ A characterization of von Neumann rings in terms of linear systems

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