On the indices in number fields and their computation for small degrees | Zendy

Abdelmejid Bayad | Zendy; Mohammed Seddik | Zendy

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On the indices in number fields and their computation for small degrees

Author(s) -

Abdelmejid Bayad,

Mohammed Seddik

Publication year - 2020

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm191025032b

Subject(s) - mathematics , conjecture , degree (music) , algebraic number field , prime (order theory) , integer (computer science) , field (mathematics) , combinatorics , dedekind cut , number theory , computation , discrete mathematics , prime number , pure mathematics , physics , algorithm , computer science , acoustics , programming language

Let K be a number field. We investigate the indices I(K) and i(K) of K introduced respectively by Dedekind and Gunji-McQuillan. Let n be a positif integer, we then prove that for any prime p ? n, there exists K a number field of degree n over Q such that p divide i(K). This result is an analogue to Bauer''s one for i(K). We compute I(K) and i(K) for cubic fields and infinite families of simplest number fields of degree less than 7. We solve questions and disprove the conjecture stated in [1].

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