The saturation of k-analytic rings and topological equivalence of associated analytic set germs (Q1059182)

Let k be an algebraically closed complete valuated field. The author calls a system of parameters \(x_ 1,...,x_ n\) of an analytic algebra A strongly separating if polynomials \(P_ j(T)\) in \(k<x_ i>[T]\) exist separable over the field of fractions of the ring \(k<x_ i>\) and with leading coefficient equal to 1 such that \(P_ j(y_ j)=0\) and \(A=k<x_ i>[y_ j]\). It is proved that saturation in the sense of Zariski with respect to a strongly separating system of parameters can be defined; if the ring A is reduced and equidimensional then it possesses a strongly separating system of parameters. It is proved that the saturation of an analytic algebra is analytic as well and the analytic set germs corresponding to these rings are topologically equivalent.