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arXiv · 2610.40185

Von Neumann regular and semisimple rings realized as principal quotients of domains

Xiaolei Zhang·Wei Qi
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Abstract

In this paper, we show that every commutative von Neumann regular ring is a quotient of a characteristic-zero Bézout domain by its principal Jacobson radical. We then characterize the commutative semisimple rings that occur as quotients of Dedekind domains. For a finite product of fields $R=\prod_{i=1}^n k_i$, such a presentation exists exactly when the cardinals $|k_i|^{\aleph_0}$ are all equal. When this condition holds, the source may be taken to be a characteristic-zero semilocal principal ideal domain, and the quotient ideal may again be its Jacobson radical.

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Xiaolei Zhang, Wei Qi. 2026-10-29. Von Neumann regular and semisimple rings realized as principal quotients of domains. https://arxiv.org/abs/2610.40185

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