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arXiv · 2506.18836

A generalization of Rao's theorem to graded $R$-subalgebras of $R[t]$

Diksha Garg·Anjan Gupta
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Abstract

Let $R$ be a Noetherian local ring of Krull dimension $d$ such that $(d!)R = R$, and let $A$ be a graded $R$-subalgebra of the polynomial algebra $R[t]$. We prove that every unimodular row of length $d + 1$ over $A$ can be completed to an invertible matrix. This is a generalization of a classical result by Rao, who proved that in the same setting, every unimodular row of length $d + 1$ over $R[t]$ admits a completion to an invertible matrix.

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Diksha Garg, Anjan Gupta. 2025-06-23. A generalization of Rao's theorem to graded $R$-subalgebras of $R[t]$. https://arxiv.org/abs/2506.18836

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