2007/12/28 by Silvio Greco, Greco, S., K. Kiyek +1
Mathematics · #13H10 (Primary) 13A18 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.0712.4329
openalex publication_date 2007/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a two-dimensional regular local ring with maximal ideal \mathfrak m, and let \wp be a simple complete \mathfrak m-primary ideal which is residually rational. Let R0:= R\subsetneqq ...\subsetneqq Rr be the quadratic sequence associated to \wp, let Γ_\wp be the value-semigroup associated to \wp, and let ((ej(\wp))0≤ j≤ r be the multiplicity sequence of \wp. We associate to \wp a sequence of natural integers, the formal characteristic sequence of \wp, and we show that the value-semigroup, the multiplicity sequence and the formal characteristic sequence are equivalent data. Furthermore, we give a new proof that Γ_\wp is symmetric, and give a formula for c_\wp, the conductor of Γ_\wp, in terms of entries of the Hamburger-Noether tableau of \wp.