2019/07/23 by Edison Marcavillaca Niño de Guzmán, de Guzmán, Edison Marcavillaca Niño, Abramo Hefez +1
Mathematics · #13H10 #14H20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13H10 #msc:14H20
paper · pdf · doi:10.48550/arxiv.1907.10666
17 pages, 2 figures. arXiv admin note: text overlap with arXiv:1804.10164
arxiv created 2019/07/23 · arxiv updated 2019/07/26
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 Fröberg.