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arXiv · 1309.4737

Laurent cancellation for rings of transcendence degree one

Gene Freudenburg
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Abstract

If $R$ is an integral domain and $A$ is an $R$-algebra, then $A$ has the {\it Laurent cancellation property over $R$} if $A^{[\pm n]}\cong_RB^{[\pm n]}$ implies $A\cong_RB$ ($n\ge 0$ and $B$ an $R$-algebra). Here, $A^{[\pm n]}$ 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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Gene Freudenburg. 2013-09-29. Laurent cancellation for rings of transcendence degree one. https://arxiv.org/abs/1309.4737

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