Perspectivity in complemented modular lattices and regular rings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915159517167616 |
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| author | Herrmann, Christian |
| author_facet | Herrmann, Christian |
| contents | Based on an analogue for systems of partial isomorphisms between lower sections in a complemented modular lattice we prove that principal right ideals $aR \cong bR$ in a (von Neumann) regular ring $R$ are perspective if
$aR \cap bR$ is of finite height in $L(R)$. This is applied to derive, for existence-varieties $\mathcal{V}$ of regular rings, equivalence of unit-regularity and direct finiteness, both conceived as a property shared by all members of $\mathcal{V}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17298 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Perspectivity in complemented modular lattices and regular rings Herrmann, Christian Rings and Algebras 06C20, 16E50 Based on an analogue for systems of partial isomorphisms between lower sections in a complemented modular lattice we prove that principal right ideals $aR \cong bR$ in a (von Neumann) regular ring $R$ are perspective if $aR \cap bR$ is of finite height in $L(R)$. This is applied to derive, for existence-varieties $\mathcal{V}$ of regular rings, equivalence of unit-regularity and direct finiteness, both conceived as a property shared by all members of $\mathcal{V}$. |
| title | Perspectivity in complemented modular lattices and regular rings |
| topic | Rings and Algebras 06C20, 16E50 |
| url | https://arxiv.org/abs/2310.17298 |