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arXiv · 2301.12681

Retracts of Laurent polynomial rings

Neena Gupta·Takanori Nagamine
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Abstract

Let $R$ be an integral domain and $B=R[x_1,\ldots,x_n]$ be the polynomial ring. In this paper, we consider retracts of $B[1/M]$ for a monomial $M$. We show that (1) if $M=\prod_{i=1}^nx_i$, then every retract is a Laurent polynomial ring over $R$, (2) if $R$ is a perfect field and $n=3$, then every retract is isomorphic to $R[y_1^{\pm1},\ldots,y_s^{\pm1},z_1,\ldots,z_t]$ for some $s,t\geq 0$.

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Neena Gupta, Takanori Nagamine. 2023-01-30. Retracts of Laurent polynomial rings. https://arxiv.org/abs/2301.12681

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