Direct finiteness of representable regular rings with involution: A counterexample
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916387716333568 |
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| author | Herrmann, Christian |
| author_facet | Herrmann, Christian |
| contents | 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 $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct finiteness of representable regular rings with involution: A counterexample Herrmann, Christian Rings and Algebras 16E50 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 $R$. |
| title | Direct finiteness of representable regular rings with involution: A counterexample |
| topic | Rings and Algebras 16E50 |
| url | https://arxiv.org/abs/2408.16437 |