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Greenberg's conjecture and Iwasawa module of real biquadratic fields I.

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Title: Greenberg's conjecture and Iwasawa module of real biquadratic fields I.
Authors: Chems-Eddin, Mohamed Mahmoud1 (AUTHOR) 2m.chemseddin@gmail.com
Source: Journal of Number Theory. Apr2026, Vol. 281, p224-266. 43p.
Subjects: Quadratic fields, Cyclotomic fields
Abstract: The main aim of this paper is to investigate Greenberg's conjecture for real biquadratic fields. More precisely, we propose the following problem: What are real biquadratic number fields k such that rank (A (k ∞)) = rank (A (k 1)) ? where A (k ∞) is the 2-Iwasawa module of k and A (k 1) is the 2-class group of k 1 the first layer of the cyclotomic Z 2 -extension of k. Moreover, we give several families of real biquadratic fields k such that A (k ∞) is trivial or isomorphic to Z / 2 n Z or Z / 2 Z × Z / 2 n Z , where n is a given positive integer. The reader can also find some results concerning the 2-rank of the class group of certain real triquadratic fields. [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
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DbLabel: Engineering Source
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  Data: Greenberg's conjecture and Iwasawa module of real biquadratic fields I.
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  Data: <searchLink fieldCode="AR" term="%22Chems-Eddin%2C+Mohamed+Mahmoud%22">Chems-Eddin, Mohamed Mahmoud</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> 2m.chemseddin@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Apr2026, Vol. 281, p224-266. 43p.
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  Data: <searchLink fieldCode="DE" term="%22Quadratic+fields%22">Quadratic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Cyclotomic+fields%22">Cyclotomic fields</searchLink>
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  Data: The main aim of this paper is to investigate Greenberg's conjecture for real biquadratic fields. More precisely, we propose the following problem: What are real biquadratic number fields k such that rank (A (k ∞)) = rank (A (k 1)) ? where A (k ∞) is the 2-Iwasawa module of k and A (k 1) is the 2-class group of k 1 the first layer of the cyclotomic Z 2 -extension of k. Moreover, we give several families of real biquadratic fields k such that A (k ∞) is trivial or isomorphic to Z / 2 n Z or Z / 2 Z × Z / 2 n Z , where n is a given positive integer. The reader can also find some results concerning the 2-rank of the class group of certain real triquadratic fields. [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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      – Type: doi
        Value: 10.1016/j.jnt.2025.09.015
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      – Code: eng
        Text: English
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        PageCount: 43
        StartPage: 224
    Subjects:
      – SubjectFull: Quadratic fields
        Type: general
      – SubjectFull: Cyclotomic fields
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      – TitleFull: Greenberg's conjecture and Iwasawa module of real biquadratic fields I.
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              Text: Apr2026
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              Y: 2026
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