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arXiv · 2408.09222

A constructive counterpart of the subdirect representation theorem for reduced rings

Ryota Kuroki
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Abstract

We give a constructive counterpart of the theorem of Andrunakievi\v{c} and Rjabuhin, which states that every reduced ring is a subdirect product of domains. As an application, we extract a constructive proof of the fact that every ring $A$ satisfying $\forall x\in A. x^3=x$ is commutative from a classical proof. We also prove a similar result for semiprime ideals.

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Ryota Kuroki. 2024-08-17. A constructive counterpart of the subdirect representation theorem for reduced rings. https://arxiv.org/abs/2408.09222

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