M. M. Chems-Eddin

activity

20192026

2

-class field towers of some multiquadratic number fields

19 citations · 71 across the 23 of their papers we have counts for

collaborators

24 papers

math.NT2026

On the class number of real multiquadratic fields

Mohamed Mahmoud Chems-Eddin, Hamza El Mamry

In their 1988 monograph, Conner and Hurrelbrink classified all real quadratic and biquadratic fields with odd class number. They also investigated real quadratic fields whose $2$ -c…

math.NT2026

On the Narrow 2-Class Field Tower of Some Real Quadratic Number Fields: Lengths Heuristics Follow-Up

Elliot Benjamin, Mohamed Mahmoud Chems-Eddin

In this article we continue the investigation of the length of the narrow $2$ -class field tower of real quadratic number fields $k$ whose discriminants are not a sum of tw…

math.NT2026

Greenberg's conjecture and Iwasawa module of Real biquadratic fields II

Mohamed Mahmoud Chems-Eddin, Hamza El Mamry

In this paper we are interested in the stability of the $2$ -rank of the class group in the cyclotomic $Z_{2}$ -extension of real biquadratic fields. In fact, we give several…

math.AC2025

Note on the Krull dimension of rings of integer-valued polynomials

M. M. Chems-Eddin, B. Feryouch, A. Tamoussit

Let $D$ be an integral domain with quotient field $K,$ $E$ a subset of $K$ and $X$ an indeterminate over $K$ . The set $Int (E, D) := {f \in K [X]; f (E) \subseteq D}$ , of inte…

math.NT2025

On the Existence of the Maximal Unramified Pro- $2$ -Extension over the Cyclotomic $Z_{2}$ -Extension with Prescribed Metacyclic Galois Group

Mohamed Mahmoud Chems-Eddin, Hamza El Mamry

For an integer $m \geq 2$ , we aim to investigate the realizability of types of metacyclic-nonmodular groups, whose abelianization is $\mathbb{Z}/2 \mathbb{Z}\times\mathbb{Z}/2^m \ma…

math.NT2025★ 1 cited

Greenberg's conjecture and Iwasawa module of Real biquadratic fields I

Mohamed Mahmoud Chems-Eddin

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…

math.NT2025★ 2 cited

On the unit group of some multiquadratic fields

Mohamed Mahmoud Chems-Eddin, Hamza El Mamry

In this paper, we calculate the unit groups and the $2$ -class numbers of the fields $K = Q (2, p_{1}, p_{2})$ and $ \mathbb{L}= \mathbb{Q}( \sqrt{…

math.AC2024

On the Krull dimension of rings of integer-valued rational functions

Mohamed Mahmoud Chems-Eddin, Badr Feryouch, Hakima Mouanis +1

Let $D$ be an integral domain with quotient field $K$ and $E$ a subset of $K$ . The \textit{ring of integer-valued rational functions on} $E$ is defined as $$\mathrm{int}_R(E,D):=\l…

math.AC2024

On rings of integer-valued rational functions

Mohamed Mahmoud Chems-Eddin, Badr Feryouch, Hakima Mouanis +1

Let $D \subseteq B$ be an extension of integral domains and $E$ a subset of the quotient field of $D$ . We introduce the ring of \textit{ $D$ -valued $B$ -rational functions on $E$ }, de…

math.NT2024

On the maximal unramified pro-2-extension of $Z_{2}$ -extension of certain real biquadratic fields

Mohamed Mahmoud Chems-Eddin

For any positive integer $n$ , we show that there exists a real number field $k$ (resp. $k^{'}$ ) of degree $2^{n + 2}$ whose $2$ -class group is isomorphic to $\mathbb{Z}/2\mathbb{Z}\time…

math.NT2024

On the unit group and the $2$ -class number of $Q (2, p, q)$

Mohamed Mahmoud Chems-Eddin, Moha Ben Taleb El Hamam, Moulay Ahmed Hajjami

Let $p \equiv 1 (mod 8)$ and $q \equiv 7 (mod 8)$ be two prime numbers. The purpose of this paper is to compute the unit group of the fields $\KK=\QQ(\sqrt 2, \sqrt{p}, \sqrt{q} )$ and…

math.NT2021

Hilbert genus fields of some number fields with high degrees

Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous

The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields $L_{m, d} := Q (ζ_{2^{m}}, d)$ , where $m\geq…

math.NT2021

Arithmetic of some real triquadratic fields; Units and 2-class groups

Mohamed Mahmoud Chems-Eddin

In this paper, we compute the unit groups and the $2$ -class numbers of the Fröhlich's triquadratic fields $\KK=\mathbb{Q}(\sqrt{2},\sqrt{p},\sqrt{q})$, where $p$ and $q$ are two pr…

math.NT2021

The construction of the Hilbert genus fields of real cyclic quartic fields

Mohamed Mahmoud Chems-Eddin, Moulay Ahmed Hajjami, Mohammed Taous

Let $p$ be a prime number such that $p = 2$ or $p \equiv 1 (mod 4)$ . Let $ε_{p}$ denote the fundamental unit of $Q (p)$ and let $a$ be a positive square-free int…

math.NT2021★ 1 cited

On Hilbert genus fields of imaginary cyclic quartic fields

Moulay Ahmed Hajjami, Mohamed Mahmoud Chems-Eddin

Let $p$ be a prime number such that $p = 2$ or $p \equiv 1 (mod 4)$ . Let $ε_{p}$ denote the fundamental unit of $Q (p)$ and let $a$ be a positive square-free int…

math.NT2020★ 2 cited

The 2-Iwasawa module over certain octic elementary fields

Mohamed Mahmoud Chems-Eddin

The aim of this paper is to determine the structure of $2$ -Iwasawa module of some imaginary triquadratic fields.

math.NT2020★ 5 cited

On the Hilbert $2$ -class field towers of some cyclotomic $Z_{2}$ -extensions

Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi

In this paper, we study the length of the $2$ -class field towers and the structure of the Galois groups $Gal (L (K_{n}) / K_{n})$ of the maximal unramified $2$ -extension…

math.NT2020★ 18 cited

Unit groups of some multiquadratic number fields and $2$ -class groups

Mohamed Mahmoud Chems-Eddin

Let $p \equiv - q \equiv 5 (mod 8)$ be two prime integers. In this paper, we investigate the unit groups of the fields $L_{1} = Q (2, p, q, - 1)$ and…

math.NT2020★ 19 cited

Units and $2$ -class field towers of some multiquadratic number fields

Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini, Abdelmalek Azizi

In this paper, we investigate the unit groups, the $2$ -class groups, the $2$ -class field towers and the structures of the second $2$ -class groups of some multiquadratic number fiel…

math.NT2020★ 4 cited

$2$ -class groups of cyclotomic towers of imaginary biquadratic fields and applications

Mohamed Mahmoud Chems-Eddin, Katharina Müller

Let $d$ be a positive square-free integer. In this paper we shall investigate the structure of the $2$ -class group of the cyclotomic $Z_{2}$ -extension of the imaginary biqua…

math.NT2020

On some imaginary triquadratic number fields $k$ with $Cl_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini

Let $d$ be a square free integer and $L_{d} := Q (ζ_{8}, d)$ . In the present work we determine all the fields $L_{d}$ such that the $2$ -class group, $Cl_{2} (L_{d})$ , o…

math.NT2020★ 5 cited

The rank of the 2-class group of some fields with large degree

Mohamed Mahmoud Chems-Eddin

Let $n \geq 3$ be an integer and $d$ an odd square-free integer. We shall compute the rank of the $2$ -class group of $L_{n, d} := Q (ζ_{2^{n}}, d)$ , when all the prime divi…

math.NT2019★ 7 cited

On the $2$ -class group of some number fields with large degree

Mohamed Mahmoud Chems-Eddin, Abdelmalek Azizi, Abdelkader Zekhnini

Let $d$ be an odd square-free integer, $m \geq 3$ any integer and $L_{m, d} := Q (ζ_{2^{m}}, d)$ . In this paper, we shall determine all the fields $L_{m, d}$ having an odd…

math.NT2019★ 7 cited

On the rank of the $2$ -class group of some imaginary triquadratic number fields

Abdelmalek Azizi, Mohamed Mahmoud Chems-Eddin, Abdelkader Zekhnini

Let $d$ be an odd square-free integer and $ζ_{8}$ a primitive $8$ -th root of unity. The purpose of this paper is to investigate the rank of the $2$ -class group of the fields $L_d=\ma…

On the class number of real multiquadratic fields

On the Narrow 2-Class Field Tower of Some Real Quadratic Number Fields: Lengths Heuristics Follow-Up

Greenberg's conjecture and Iwasawa module of Real biquadratic fields II

Note on the Krull dimension of rings of integer-valued polynomials

On the Existence of the Maximal Unramified Pro-2-Extension over the Cyclotomic Z2​-Extension with Prescribed Metacyclic Galois Group

Greenberg's conjecture and Iwasawa module of Real biquadratic fields I

On the unit group of some multiquadratic fields

On the Krull dimension of rings of integer-valued rational functions

On rings of integer-valued rational functions

On the maximal unramified pro-2-extension of Z2​-extension of certain real biquadratic fields

On the unit group and the 2-class number of Q(2​,p​,q​)

Hilbert genus fields of some number fields with high degrees

Arithmetic of some real triquadratic fields; Units and 2-class groups

The construction of the Hilbert genus fields of real cyclic quartic fields

On Hilbert genus fields of imaginary cyclic quartic fields

The 2-Iwasawa module over certain octic elementary fields

On the Hilbert 2-class field towers of some cyclotomic Z2​-extensions

Unit groups of some multiquadratic number fields and 2-class groups

Units and 2-class field towers of some multiquadratic number fields

2-class groups of cyclotomic towers of imaginary biquadratic fields and applications

On some imaginary triquadratic number fields k with Cl2​(k)≃(2,4) or (2,2,2)

The rank of the 2-class group of some fields with large degree

On the 2-class group of some number fields with large degree

On the rank of the 2-class group of some imaginary triquadratic number fields

On the Existence of the Maximal Unramified Pro- $2$ -Extension over the Cyclotomic $Z_{2}$ -Extension with Prescribed Metacyclic Galois Group

On the maximal unramified pro-2-extension of $Z_{2}$ -extension of certain real biquadratic fields

On the unit group and the $2$ -class number of $Q (2, p, q)$

On the Hilbert $2$ -class field towers of some cyclotomic $Z_{2}$ -extensions

Unit groups of some multiquadratic number fields and $2$ -class groups

Units and $2$ -class field towers of some multiquadratic number fields

$2$ -class groups of cyclotomic towers of imaginary biquadratic fields and applications

On some imaginary triquadratic number fields $k$ with $Cl_{2} (k) ≃ (2, 4)$ or $(2, 2, 2)$

On the $2$ -class group of some number fields with large degree

On the rank of the $2$ -class group of some imaginary triquadratic number fields