  The main result in this paper is to supply a recursive formula, on the number
of minimal primes, for the colength of a fractional ideal in terms of the
maximal points of the value set of the ideal itself. The fractional ideals are
taken in the class of complete admissible rings, a more general class of rings
than those of algebroid curves. For such rings with two or three minimal
primes, a closed formula for that colength is provided, so improving results by
Barucci, D'Anna and Fr\"oberg.

Algebraic Geometry;Commutative Algebra