On ideal class groups of totally degenerate number rings

2025/05/04 by Ruben Hambardzumyan, Hambardzumyan, Ruben, Mihran Papikian +1
Computer Science · Mathematics · #11R29 #11R54 #15B36 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2505.09635

openalex publication_date 2025/05/04 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

Let χ(x)∈ ℤ[x] be a monic polynomial whose roots are distinct integers. We study the ideal class monoid and the ideal class group of the ring ℤ[x]/(χ(x)). We obtain formulas for the orders of these objects, and study their asymptotic behavior as the discriminant of χ(x) tends to infinity, in analogy with the Brauer-Siegel theorem. Finally, we describe the structure of the ideal class group when the degree of χ(x) is 2 or 3.

Citations

• Computation of lattice isomorphisms and the integral matrix similarity problem

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