On the number of generators of modules over Laurent rings (Q1201421)

The author proves the following theorem: Let \(B=A[X_ 1,\dots,X_ n,Y_ i^{\pm 1},\dots,Y_ m^{\pm 1}]\) be a Laurent polynomial ring and let \(M\) be a \(B\)-module of constant rank \(r\). Then \[ \mu(M)\leq\max\{\dim A+r,\mu(M_ P)+\dim B-htP\} \] where \(P\) runs over the prime ideals of \(B\) at which \(M_ P\) is not free and \(\mu\) denotes the minimal number of generators. This generalises results of various authors including the author's result in this direction on polynomial rings [Math. Z. 208, No. 1, 11-21 (1991; Zbl 0738.13013)]. The author uses techniques developed by him and \textit{H. Lindel} on analytic isomorphisms and semilinear maps to achieve this.