Perspectivity in complemented modular lattices and regular rings
| Autor: | Herrmann, Christian |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\mathcal{V}$. |
| Databáze: | arXiv |
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