Elasticity of orders with prime conductor.
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| Title: | Elasticity of orders with prime conductor. |
|---|---|
| Authors: | Kettinger, Jared1 (AUTHOR), Moles, Grant1,2 (AUTHOR) gramoles@gmail.com |
| Source: | Journal of Number Theory. Feb2026, Vol. 279, p579-593. 15p. |
| Subjects: | Class groups (Mathematics), Prime ideals, Mathematical analysis, Ideals (Algebra), Rings of integers, Factorization, Scientific observation |
| Abstract: | Let R be an order in a number field whose conductor ideal P : = (R : R ‾) is prime in the ring of integers R ‾. In this paper, we explore the factorization properties of such orders. Most notably, we give a complete characterization of the elasticity of R in terms of its class group. We conclude with an application to the computation of class groups of certain orders. • Elasticity of an order with prime conductor is determined. • Elasticity depends only on the class group structure. • Class group structure can be determined in certain special cases. • Examples of known elasticities and class groups are given. [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 |
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| Header | DbId: egs DbLabel: Engineering Source An: 187866152 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Elasticity of orders with prime conductor. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kettinger%2C+Jared%22">Kettinger, Jared</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Moles%2C+Grant%22">Moles, Grant</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> gramoles@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Feb2026, Vol. 279, p579-593. 15p. – 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="%22Prime+ideals%22">Prime ideals</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Ideals+%28Algebra%29%22">Ideals (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Rings+of+integers%22">Rings of integers</searchLink><br /><searchLink fieldCode="DE" term="%22Factorization%22">Factorization</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+observation%22">Scientific observation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let R be an order in a number field whose conductor ideal P : = (R : R ‾) is prime in the ring of integers R ‾. In this paper, we explore the factorization properties of such orders. Most notably, we give a complete characterization of the elasticity of R in terms of its class group. We conclude with an application to the computation of class groups of certain orders. • Elasticity of an order with prime conductor is determined. • Elasticity depends only on the class group structure. • Class group structure can be determined in certain special cases. • Examples of known elasticities and class groups are given. [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jnt.2025.07.013 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 579 Subjects: – SubjectFull: Class groups (Mathematics) Type: general – SubjectFull: Prime ideals Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Ideals (Algebra) Type: general – SubjectFull: Rings of integers Type: general – SubjectFull: Factorization Type: general – SubjectFull: Scientific observation Type: general Titles: – TitleFull: Elasticity of orders with prime conductor. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kettinger, Jared – PersonEntity: Name: NameFull: Moles, Grant IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 0022314X Numbering: – Type: volume Value: 279 Titles: – TitleFull: Journal of Number Theory Type: main |
| ResultId | 1 |
