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.
Categories: math.AC