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arXiv · 2608.26044

Polynomial extensions do not preserve the strong finite type property

Viet-Hoang Tran·Phan Thanh Toan·Thieu N. Vo·Tan M. Nguyen
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Abstract

Arnold introduced the strong finite type (SFT) property in 1973 while studying the dimension of power series rings. For several classes of rings, polynomial extension is known to preserve the SFT property, but the general question remained open. We answer it negatively by constructing an SFT ring $R$ such that $R[X]$ is not SFT.

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Viet-Hoang Tran, Phan Thanh Toan, Thieu N. Vo, Tan M. Nguyen. 2026-08-26. Polynomial extensions do not preserve the strong finite type property. https://arxiv.org/abs/2608.26044

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