Open AccessOn the indices in number fields and their computation for small degrees
Author(s) -
Abdelmejid Bayad,
Mohammed Seddik
Publication year - 2021
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].