Author:
Author:
Lhoussain El Fadil
lhouelfadil2@gmail.com
Lhoussain El Fadil
Faculty of Sciences Dhar El Mahraz, P.O. Box 1874 Atlas-Fes, Sidi mohamed ben Abdellah University, Morocco
Search for other papers by Lhoussain El Fadil in
Current site
Google Scholar
PubMed
Search for other papers by Lhoussain El Fadil in
Current site
Google Scholar
PubMed
Abstract
Let K = ℚ(α) be a number field generated by a complex root α of a monic irreducible polynomial f(x) = x24 – m, with m ≠ 1 is a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≢∓1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), then the number field K is not monogenic.
ProCite
RefWorks
Reference Manager
BibTeX
Zotero
EndNote
-
[1]
Ahmad, S., Nakahara, T. and Husnine, S. M., Power integral bases for certain pure sextic fields, Int. J. of Number Theory, 8v:10 (2014), 2257- 2265.
-
[2]
Ahmad, S., Nakahara, T. and Hameed, A., On certain pure sextic fields related to a problem of Hasse, Int. J. Alg. and Comput., 26(3) (2016), 577-583.
-
[3]
Hameed, A. and Nakahara, T., Integral bases and relative monogenity of pure octic fields, Bull. Math. Soc. Sci. Math. Roumanie, 58(106) (2015), 419-433.
-
[4]
Cohen, H., A Course in Computational Algebraic Number Theory, GTM 138, Springer-Verlag Berlin Heidelberg (1993)
-
[5]
El Fadil, L., Computation of a power integral basis of a pure cubic number field, Int. J. Contemp. Math. Sci., 2(13-16)(2007), 601-606.
-
[6]
El Fadil, L., On Power integral bases for certain pure number fields (preprint).
-
[7]
El Fadil, L., On Newton polygon’s techniques and factorization of polynomial over henselian valued fields, J. of Algebra and its Appl. (2020), doi:S0219498820501881
-
[8]
El Fadil, L., Montes, J. and Nart, E., Newton polygons and p-integral bases of quartic number fields, J. Algebra and Appl., 11(4) (2012), 1250073.
-
[9]
Funakura, T., On integral bases of pure quartic fields, Math. J. Okayama Univ., 26(1984), 27-41.
-
[10]
GaÁl, I., Power integral bases in algebraic number fields, Ann. Univ. Sci. Budapest. Sect. Comp., 18 (1999), 61-87.
-
[11]
GaÁl, I., Diophantine equations and power integral bases, Theory and algorithm, Second edition, Boston, Birkhäuser, 2019.
-
[12]
GaÁl, I., Olajos, P. and Pohst, M., Power integral bases in orders of composite fields, Exp. Math., 11(1) (2002), 87-90.
-
[13]
GaÁl, I. and Remete, L., Binomial Thue equations and power integral bases in pure quartic fields, JP Journal of Algebra Number Theory Appl., 32(1) (2014), 49-61.
-
[14]
GaÁl, I. and Remete, L., Power integral bases and monogenity of pure fields, J. of Number Theory, 173 (2017), 129-146.
-
[16]
Hensel, K., Theorie der algebraischen Zahlen, Teubner Verlag, LeipzigBerlin, 1908.
-
[17]
Motoda, Y., Nakahara, T. and Shah, S. I. A., On a problem of Hasse, J. Number Theory, 96 (2002), 326-334.
-
[18]
Narkiewicz, W., Elementary and Analytic Theory of Algebraic Numbers, Third Edition, Springer, 2004.
-
[19]
Ore, O., Newtonsche Polygone in der Theorie der algebraischen Korper, Math. Ann., 99 (1928), 84-117.
-
[20]
Pethö, A. and Pohst, M., On the indices of multiquadratic number fields, Acta Arith., 153(4) (2012), 393-414.
-
[21]
Dedekind, R., Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der hoheren Kongruenzen, Göttingen Abhandlungen, 23 (1878), 1-23.
Editors in Chief
Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)
Managing Editor
Gábor SÁGI (Rényi Institute of Mathematics)
Editorial Board
- Imre BÁRÁNY (Rényi Institute of Mathematics)
- Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
- Péter CSIKVÁRI (ELTE, Budapest)
- Joshua GREENE (Boston College)
- Penny HAXELL (University of Waterloo)
- Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
- Ron HOLZMAN (Technion, Haifa)
- Satoru IWATA (University of Tokyo)
- Tibor JORDÁN (ELTE, Budapest)
- Roy MESHULAM (Technion, Haifa)
- Frédéric MEUNIER (École des Ponts ParisTech)
- Márton NASZÓDI (ELTE, Budapest)
- Eran NEVO (Hebrew University of Jerusalem)
- János PACH (Rényi Institute of Mathematics)
- Péter Pál PACH (BME, Budapest)
- Andrew SUK (University of California, San Diego)
- Zoltán SZABÓ (Princeton University)
- Martin TANCER (Charles University, Prague)
- Gábor TARDOS (Rényi Institute of Mathematics)
- Paul WOLLAN (University of Rome "La Sapienza")
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu
Indexing and Abstracting Services:
- CABELLS Journalytics
- CompuMath Citation Index
- Essential Science Indicators
- Mathematical Reviews
- Science Citation Index Expanded (SciSearch)
- SCOPUS
- Zentralblatt MATH
| 2023 | |
|---|---|
| Web of Science | |
| Journal Impact Factor | 0.4 |
| Rank by Impact Factor | Q4 (Mathematics) |
| Journal Citation Indicator | 0.49 |
| Scopus | |
| CiteScore | 1.3 |
| CiteScore rank | Q2 (General Mathematics) |
| SNIP | 0.705 |
| Scimago | |
| SJR index | 0.239 |
| SJR Q rank | Q3 |
| Studia Scientiarum Mathematicarum Hungarica | |
|---|---|
| Publication Model | Hybrid |
| Submission Fee | none |
| Article Processing Charge | 900 EUR/article (only for OA publications) |
| Printed Color Illustrations | 40 EUR (or 10 000 HUF) + VAT / piece |
| Regional discounts on country of the funding agency | World Bank Lower-middle-income economies: 50% World Bank Low-income economies: 100% |
| Further Discounts | Editorial Board / Advisory Board members: 50% Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100% |
| Subscription fee 2025 | Online subsscription: 796 EUR / 876 USD Print + online subscription: 900 EUR / 988 USD |
| Subscription Information | Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content. |
| Purchase per Title | Individual articles are sold on the displayed price. |
| Studia Scientiarum Mathematicarum Hungarica | |
|---|---|
| Language | English French German |
| Size | B5 |
| Year of Foundation |
1966 |
| Volumes per Year |
1 |
| Issues per Year |
4 |
| Founder | Magyar Tudományos Akadémia  |
| Founder's Address |
H-1051 Budapest, Hungary, Széchenyi István tér 9. |
| Publisher | Akadémiai Kiadó |
| Publisher's Address |
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. |
| Responsible Publisher |
Chief Executive Officer, Akadémiai Kiadó |
| ISSN | 0081-6906 (Print) |
| ISSN | 1588-2896 (Online) |
Monthly Content Usage
| Abstract Views | Full Text Views | PDF Downloads | |
|---|---|---|---|
| Sep 2024 | 16 | 0 | 0 |
| Oct 2024 | 54 | 0 | 0 |
| Nov 2024 | 22 | 0 | 0 |
| Dec 2024 | 19 | 0 | 0 |
| Jan 2025 | 24 | 0 | 0 |
| Feb 2025 | 14 | 0 | 0 |
| Mar 2025 | 0 | 0 | 0 |
Author:
Author:
Author:
Author:
Copyright Akadémiai Kiadó AKJournals is the trademark of Akadémiai Kiadó's journal publishing business branch.
Powered by PubFactory