The reduced ideals of a special order in a pure cubic number field
Abdelmalek Azizi; Jamal Benamara; Moulay Chrif Ismaili; Mohammed Talbi
Archivum Mathematicum (2020)
- Volume: 056, Issue: 3, page 171-182
- ISSN: 0044-8753
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topAzizi, Abdelmalek, et al. "The reduced ideals of a special order in a pure cubic number field." Archivum Mathematicum 056.3 (2020): 171-182. <http://eudml.org/doc/296993>.
@article{Azizi2020,
abstract = {Let $K=\mathbb \{Q\}(\theta )$ be a pure cubic field, with $\theta ^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $\mathcal \{O\}=\mathbb \{Z\}[\theta ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $\lnot \equiv \pm 1\hspace\{4.44443pt\}(\@mod \; 9)$.},
author = {Azizi, Abdelmalek, Benamara, Jamal, Ismaili, Moulay Chrif, Talbi, Mohammed},
journal = {Archivum Mathematicum},
keywords = {cubic field; reduced ideal},
language = {eng},
number = {3},
pages = {171-182},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The reduced ideals of a special order in a pure cubic number field},
url = {http://eudml.org/doc/296993},
volume = {056},
year = {2020},
}
TY - JOUR
AU - Azizi, Abdelmalek
AU - Benamara, Jamal
AU - Ismaili, Moulay Chrif
AU - Talbi, Mohammed
TI - The reduced ideals of a special order in a pure cubic number field
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 3
SP - 171
EP - 182
AB - Let $K=\mathbb {Q}(\theta )$ be a pure cubic field, with $\theta ^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $\mathcal {O}=\mathbb {Z}[\theta ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $\lnot \equiv \pm 1\hspace{4.44443pt}(\@mod \; 9)$.
LA - eng
KW - cubic field; reduced ideal
UR - http://eudml.org/doc/296993
ER -
References
top- Alaca, S., Williams, K.S., Introductory algebraic number theory, Cambridge University Press, Cambridge, UK, 2004. (2004) MR2031707
- Buchmann, J.A., Scheidler, R., Williams, H.C., Implementation of a key exchange protocol using real quadratic fields, Advances in Cryptography–EUROCRYPT'90. EUROCRYPT 1990. Lecture Notes in Computer Science (Damgård, I.B., ed.), vol. 473, Springer, Berlin, Heidelberg, 1991, pp. 98–109. (1991) MR1102474
- Buchmann, J.A., Williams, H.C., 10.1007/BF02351719, J. Cryptology 1 (1988), 107–118. (1988) MR0972575DOI10.1007/BF02351719
- Buchmann, J.A., Williams, H.C., 10.1090/S0025-5718-1988-0929554-6, Math. Comp. 50 (182) (1988), 569–579. (1988) MR0929554DOI10.1090/S0025-5718-1988-0929554-6
- Buchmann, J.A., Williams, H.C., A sub exponential algorithm for the determination of class groups and regulators of algebraic number fields, Seminaire de Theorie des Nombres, Paris 1988–1989, Progr. Math., vol. 91, Birkhauser Boston, Boston, MA, 1990, pp. 27–41. (1990) MR1104698
- Cohen, H., A course in computational algebraic number theory, Springer–Verlag, 1996. (1996) MR1228206
- Jacobs, G.T., Reduced ideals and periodic sequences in pure cubic fields, Ph.D. thesis, University of North Texas, 2015, August 2015, https://digital.library.unt.edu/ark:/67531/metadc804842. (2015) MR3503469
- Mollin, R., Quadratics, CRC Press, Inc., Boca Raton, Florida, 1996. (1996) Zbl0888.11041MR1383823
- Neukirch, J., Algebraic Number Theory, Springer–Verlag Berlin, Heidelberg, 1999. (1999) Zbl0956.11021MR1697859
- Payan, J., Sur le groupe des classes d’un corps quadratique, Cours de l'institut Fourier 7 (1972), 2–30. (1972)
- Prabpayak, C., Orders in pure cubic number fields, Ph.D. thesis, Univ. Graz. Grazer Math. Ber. 361, 2014. (2014) MR3364308
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