Power bases for cyclotomic integer rings

DOI10.1006/jnth.1997.2214zbMath0923.11150OpenAlexW1971717009MaRDI QIDQ1267295

Leanne Robertson

Publication date: 13 October 1999

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2214

zbMATH Keywords

power integral basescyclotomic fieldsBremner's conjecture

Mathematics Subject Classification ID

Iwasawa theory (11R23) Cyclotomic extensions (11R18) Algebraic numbers; rings of algebraic integers (11R04)

Related Items

Bases of canonical number systems in quartic algebraic number fields, On Multiplicative Independent Bases for Canonical Number Systems in Cyclotomic Number Fields, Generators of the ring of integers of a cyclotomic extension, Power integral bases in prime-power cyclotomic fields, A hybrid Gröbner bases approach to computing power integral bases, Power integral bases for real cyclotomic fields, Power bases for 2-power cyclotomic fields, MONOGENEITY IN CYCLOTOMIC FIELDS, On a problem of Hasse for certain imaginary Abelian fields

Cites Work

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• On the resolution of index form equations in sextic fields with an imaginary quadratic subfield
• On the indices and integral bases of non-cyclic but Abelian biquadratic fields
• Integral generators in a certain quartic field and related diophantine equations
• On power bases in cyclotomic number fields
• On the resolution of index form equations in biquadratic number fields. III: The bicyclic biquadratic case
• Simultaneous representation of integers by a pair of ternary quadratic forms -- with an application to index form equations in quartic number fields
• Sur les discriminants des nombres algébriques
• Computing All Power Integral Bases of Cubic Fields
• Computing all power integral bases in orders of totally real cyclic sextic number fields
• Maillet’s determinant