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arXiv · 2408.16437

Direct finiteness of representable regular rings with involution: A counterexample

Christian Herrmann
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Abstract

Bruns and Roddy constructed a $3$-generated modular ortholattice $L$ which cannot be embedded into any complete modular ortholattice. Motivated by their approach, we use shift operators to construct a $*$-regular $*$-ring $R$ of endomorphisms of an inner product space (which can be chosen as the Hilbert space $\ell^2$) such that direct finiteness fails for $R$.

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Christian Herrmann. 2024-08-29. Direct finiteness of representable regular rings with involution: A counterexample. https://arxiv.org/abs/2408.16437

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