Ramification index and multiplicity

Abstract

Now let a0 be the family of pairs, R c S of local, integrally closed domains such that S is an R-algebra. We show ia Section i that r(S/R) on a0 is an integral-valued function having the properties given above. In Section 2 we show that r(S/R) is the only integral-valued function having these properties, and we also give another way of computing r(S/R) for R c S in a0 using the notion of a fibre algebra. The paper then concludes with a discussion of tame ramification in terms of the reduced ramification index given above.