View in EDS

On ideal class groups of totally degenerate number rings.

Saved in:
Bibliographic Details
Title: On ideal class groups of totally degenerate number rings.
Authors: Hambardzumyan, Ruben1 (AUTHOR) ruben.hambardzumyan2@edu.ysu.am, Papikian, Mihran1,2 (AUTHOR) papikian@psu.edu
Source: Journal of Number Theory. May2026, Vol. 282, p118-143. 26p.
Subjects: Class groups (Mathematics), Polynomials, Asymptotic expansions, Ordered algebraic structures, Integers
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. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 190715546
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On ideal class groups of totally degenerate number rings.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Hambardzumyan%2C+Ruben%22">Hambardzumyan, Ruben</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> ruben.hambardzumyan2@edu.ysu.am</i><br /><searchLink fieldCode="AR" term="%22Papikian%2C+Mihran%22">Papikian, Mihran</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> papikian@psu.edu</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. May2026, Vol. 282, p118-143. 26p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Class+groups+%28Mathematics%29%22">Class groups (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Asymptotic+expansions%22">Asymptotic expansions</searchLink><br /><searchLink fieldCode="DE" term="%22Ordered+algebraic+structures%22">Ordered algebraic structures</searchLink><br /><searchLink fieldCode="DE" term="%22Integers%22">Integers</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=190715546
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.11.001
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 118
    Subjects:
      – SubjectFull: Class groups (Mathematics)
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Asymptotic expansions
        Type: general
      – SubjectFull: Ordered algebraic structures
        Type: general
      – SubjectFull: Integers
        Type: general
    Titles:
      – TitleFull: On ideal class groups of totally degenerate number rings.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Hambardzumyan, Ruben
      – PersonEntity:
          Name:
            NameFull: Papikian, Mihran
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 0022314X
          Numbering:
            – Type: volume
              Value: 282
          Titles:
            – TitleFull: Journal of Number Theory
              Type: main
ResultId 1