Retracts of Laurent polynomial rings

2023/01/30 by Gupta, Neena, Nagamine, Takanori
Mathematics · #13B25 (Primary) #14A05 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2301.12681

openalex publication_date 2023/01/30 · openalex created_date 2023/02/01 · openalex updated_date 2026/07/28

Abstract

Let R be an integral domain and B=R[x₁,…,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=∏_i=1ⁿx_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[y₁^±1,…,y_s^±1,z₁,…,z_t] for some s,t≥ 0.

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