Direct finiteness of representable regular rings with involution

2019/01/11 by Herrmann, Christian
#16E50 #16W10 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1901.03555

Abstract

For von Neumann *-regular rings R of endomorphisms (the involution given by taking adjoints) of inner product spaces we provide a condition on r in R (in terms of action of r on finite dimensional subspaces) for r being a unit. It remains open whether this result can be used to prove direct finiteness of R. This was claimed in earlier versions but no proof was given.

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