带内卷的可表示正则环的直接有限性：一个反例

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-29 DOI:arxiv-2408.16437

Christian Herrmann

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引用次数: 0

摘要

布鲁恩斯和罗迪构建了一个$3$生成的模块正网格$L$，它不能嵌入到任何完整的模块正网格中。受他们方法的启发，我们使用移位算子来构造一个内积空间（可以选择为希尔贝空间 $\ell^2$）的内变换的 $*$-regular $*$-ring $R$，从而使直接有限性对 $R$ 失效。

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Direct finiteness of representable regular rings with involution: A counterexample

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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arXiv - MATH - Rings and Algebras

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