On the Colength of Fractional Ideals

E. M. N. de Guzmán and A. Hefez

Journal of Singularities
volume 21 (2020), 119-131

Received: 25 April 2018. Received in revised form: 13 March 2019.

DOI: 10.5427/jsing.2020.21g

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Abstract:

The main goal of this paper is to give a recursive formula for the colength of a fractional ideal in terms of some maximal points of its value set and of its projections. The fractional ideals are relative to a class of rings called admissible, a more general class of one dimensional local rings that contains those of algebroid curves. For fractional ideals of such rings with two or three minimal primes, a closed formula for the colength is provided.

2010 Mathematical Subject Classification:

13H10, 14H20

Key words and phrases:

Admissible rings, Algebroid curves, Fractional ideals, Value sets of ideals, Colength of ideals

Author(s) information:

E. M. N. de Guzmán	A. Hefez
Departamento de Matemática Aplicada	Departamento de Matemática Aplicada
Universidade Federal Fluminense	Universidade Federal Fluminense
Brazil	Brazil
email: e.marcavillaca@gmail.com	email: ahefez@id.uff.br