Laurent cancellation for rings of transcendence degree one

2013/09/18 by Gene Freudenburg, Freudenburg, Gene
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1309.4737

openalex publication_date 2013/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If R is an integral domain and A is an R-algebra, then A has the \it Laurent cancellation property over R if A^{[± n]}≅_RB^{[± n]} implies A≅_RB (n≥ 0 and B an R-algebra). Here, A^{[± n]} denotes the ring of Laurent polynomials in n variables over A. Our main result (Thm. 4.3) is that, if the transcendence degree of A over R is one, then A has the Laurent cancellation property. The proof uses the characterization of Laurent polynomial rings given in Thm. 3.2.

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