Cyclic Galois extensions of regular local rings (Q915785)

Let S be the integral closure of a ring of formal power series ring R in d indeterminates over an algebraically closed field, in a finite, abelian Galois extension L of the field of fractions K of R, such that the order of the Galois group \(G=Gal(K,L)\) is prime to the characteristic \(p\) of K. One gives here a characterization of the invertibility of the structural constants \(g(\chi,\chi')\in R\) defined by the R-algebra structure of the free R-module S, and consequently a method to calculate the embedding dimension and the Cohen-Macaulay type of S. Here \(\chi\) and \(\chi'\) run in the set of characters of G.