Hasse’s problem for monogenic fields

Toru Nakahara

doi:10.5802/ambp.252

Toru Nakahara ¹

¹ Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan. Current address: NUCES, Peshawar Campus, 160-Industrial Estate, Hayatabad, Peshawar, N.W.F.P. The Islamic Republic of Pakistan

Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 47-56.

Résumé

In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [7] [9], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [15].

MR Zbl

DOI : 10.5802/ambp.252

Classification : 11R27, 11R29, 11R37
Keywords: Power integral basis, monogenic fields, Hasse’s problem
Mots clés : remplir svp

Affiliations des auteurs :

Toru Nakahara ¹

¹ Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga 840-8502, Japan. Current address: NUCES, Peshawar Campus, 160-Industrial Estate, Hayatabad, Peshawar, N.W.F.P. The Islamic Republic of Pakistan

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     title = {Hasse{\textquoteright}s problem for monogenic fields},
     journal = {Annales math\'ematiques Blaise Pascal},
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     publisher = {Annales math\'ematiques Blaise Pascal},
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     zbl = {1187.11038},
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     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.252/}
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Toru Nakahara. Hasse’s problem for monogenic fields. Annales mathématiques Blaise Pascal, Tome 16 (2009) no. 1, pp. 47-56. doi : 10.5802/ambp.252. https://ambp.centre-mersenne.org/articles/10.5802/ambp.252/

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