Hasse’s problem for monogenic fields
Annales mathématiques Blaise Pascal, Volume 16 (2009) no. 1, pp. 47-56.

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].

DOI: 10.5802/ambp.252
Classification: 11R27,  11R29,  11R37
Keywords: Power integral basis, monogenic fields, Hasse’s problem
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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Toru Nakahara. Hasse’s problem for monogenic fields. Annales mathématiques Blaise Pascal, Volume 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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[15] K.H. Park; Y. Motoda; T. Nakahara On integral bases of certain octic abelian fields (Submitted)

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