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Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

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[1] AHMAD, S.—NAKAHARA, T.– HUSNINE, S. M. HUSNINE: Power integral bases for certain pure sextic fields, Int.J.NumberTheory 10, (2014), no. 8, 2257–2265.Search in Google Scholar

[2] AHMAD, S.—NAKAHARA, T.—HAMEED, A.: On certain pure sextic fields related to a problem of Hasse,Int.J.Alg.Comput., 26, No 3 (2016), no. 3, 577–583 .Search in Google Scholar

[3] ALACA, S.: p-integral bases of a cubic field, Proc. Am. Math. Soc. 126 (1998), 1949–1953.10.1090/S0002-9939-98-04422-0Search in Google Scholar

[4] ALACA, S.—WILLIAMS, K.: p-integral bases of a quartic field defined by a trinomial x4 + ax + b, Far. East. J. Math. Sci. 12 (2004), 137–168.Search in Google Scholar

[5] HAMEED, A.—NAKAHARA, T.: Integral bases and relative monogenity of pure octic fields, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 58(106) (2015), no. 4, 419–433.Search in Google Scholar

[6] CHARKANI, M. E.—SAHMOUDI, M.: Sextic extension with cubic subfield,JPJ.Algebra Number Theory Appl. 34 (2014), no. 2, 139–150.Search in Google Scholar

[7] COHEN, H.: A Course in Computational Algebraic Number Theory, GTM 138, Springer-Verlag, Berlin, 1993.10.1007/978-3-662-02945-9Search in Google Scholar

[8] DEDEKIND, R.: Über den Zusammenhang zwischen der Theorie der Ideale und der Theorie der höheren Congruenzen,Göttingen Abhandlungen, 23 (1878), 1–23.Search in Google Scholar

[9] EL FADIL, L.: Computation of a power integral basis of a pure cubic number field,Int. J. Contemp. Math. Sci. 2 (2007), 601–606.10.12988/ijcms.2007.07058Search in Google Scholar

[10] EL FADIL, L.: Prime ideal factorization and p-integral basis of quintic number fields defined by X5 + aX + b,GulfJ.Math. 6 (2018), no. 4, 1–13.Search in Google Scholar

[11] EL FADIL, L.: On Power integral bases for certain pure sextic fields, Bol. Soc. Paran. Math. (to appear)Search in Google Scholar

[12] EL FADIL, L.: On Power integral bases for certain pure sextic fields with non-square free coeffcients, J. Number Theory, 228 (2021), 375–389.10.1016/j.jnt.2021.03.025Search in Google Scholar

[13] EL FADIL, L.: On Newton polygon’s techniques and factorization of polynomial over Henselian valued fields, J. of Algebra and its Appl. 19 (2020), no. 10, Article id. 2050188. https://doi.org/10.1142/S021949882050188110.1142/S0219498820501881Search in Google Scholar

[14] EL FADIL, L.—GA ÁL, I.: On integral bases and monogeneity of pure octic number fields with non-square free parameters, Glasnik Mat. (submitted) arXiv preprint, arXiv:2202.04417, 2022.Search in Google Scholar

[15] EL FADIL, L.—MONTES, J.—NART, E.: Newton polygons and p-integral bases of quartic number fields, J. Algebra and Appl. 11 (2012), no. 4, Article id. 1250073. https://doi.org/10.1142/S021949881250073910.1142/S0219498812500739Search in Google Scholar

[16] FUNAKURA, T.: On integral bases of pure quartic fields, Math. J. Okayama Univ. 26 (1984), 27–41.Search in Google Scholar

[17] GA ÁL, I.: Diophantine Equations and Power Integral Bases. Theory and Algorithms. 2nd edition, Birkh¨auser/Springer, Cham, 2019.10.1007/978-3-030-23865-0Search in Google Scholar

[18] GA ÁL, I. — GY ŐRY, K.: Index form equations in quintic fields,Acta Arith. 89 (1999), 379–396.10.4064/aa-89-4-379-396Search in Google Scholar

[19] GA ÁL,I.—REMETE,L.: Binomial Thue equations and power integral bases in pure quartic fields, JP J. Algebra Number Theory Appl. 32 (2014), no. 1, 49–61.Search in Google Scholar

[20] GA ÁL, I.—REMETE, L.: Power integral bases and monogenity of pure fields,J.Number Theory, 173 (2017), 129–146.10.1016/j.jnt.2016.09.009Search in Google Scholar

[21] GU ÀRDIA, J.—MONTES, J.—NART, E.: Newton polygons of higher order in algebraic number theory, Trans. Amer. Math. Soc. 364 (2012), no. 1, 361–416.Search in Google Scholar

[22] HASSE, H.: Zahlentheorie. Akademie-Verlag, Berlin, 1963.10.1515/9783112478202Search in Google Scholar

[23] HENSEL, K.: Theorie der algebraischen Zahlen. Teubner Verlag, Leipzig, Berlin, 1908.Search in Google Scholar

[24] MACLANE, S.: A construction for absolute values in polynomial rings,Trans.Amer. Math. Soc. 40 (1936), 363–395.10.1090/S0002-9947-1936-1501879-8Search in Google Scholar

[25] MONTES, J.—NART, E.: On a theorem of Ore,J.Algebra, 146 (1992), no. 2, 318–334.Search in Google Scholar

[26] MOTODA, Y.—NAKAHARA, T.—SHAH, S. I. A.: On a problem of Hasse,J. Number Theory, 96 (2002), 326–334.10.1006/jnth.2002.2805Search in Google Scholar

[27] NEUKIRCH, J.: Algebraic Number Theory, Springer-Verlag, Berlin, 1999.10.1007/978-3-662-03983-0Search in Google Scholar

[28] ORE, O.: Newtonsche Polygone in der Theorie der algebraischen Körper, Math. Ann. 99 (1928), 84–117.10.1007/BF01459087Search in Google Scholar

[29] PETH Ő, A.—POHST, M.: On the indices of multiquadratic number fields,Acta Arith. 153 (2012), no. 4, 393–414.Search in Google Scholar

eISSN:
1338-9750
Lingua:
Inglese
Frequenza di pubblicazione:
3 volte all'anno
Argomenti della rivista:
Mathematics, General Mathematics