On common index divisors and monogenity of septic number fields defined by trinomials of type \(x^7 + ax^2 + b\)

Other number fields (11R21) Algebraic number theory computations (11Y40) Cubic and quartic extensions (11R16) Algebraic numbers; rings of algebraic integers (11R04)

Cites Work

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Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
On biquadratic fields that admit unit power integral basis
On a theorem of Ore
On the resolution of index form equations in quartic number fields
Newtonsche Polygone in der Theorie der algebraischen Körper.
Zur Theorie der außerwesentlichen Diskriminantenteiler algebraischer Körper.
Arithmetische Untersuchungen über Discriminanten und ihre ausserwesentlichen Teiler.
On the common index divisors of an algebraic field.
On monogenity of certain number fields defined by \(x^8+ax+b\)
On certain pure sextic fields related to a problem of Hasse
Discriminant equations in Diophantine number theory
Multiply monogenic orders
On the indices of multiquadratic number fields
Power integral bases for certain pure sextic fields
Unit Equations in Diophantine Number Theory
Effective Determination of the Decomposition of the Rational Primes in a Cubic Field
On the Index of a Number Field
On discriminants and indices of integers of an algebraic number field.
Index form equations in quintic fields
The Story of Algebraic Numbers in the First Half of the 20th Century
The index of a quartic field defined by a trinomial X4 + aX + b
Infinite families of monogenic trinomials and their Galois groups
Characterization of primes dividing the index of a trinomial
Index form equations in sextic fields: a hard computation
AN EXPERIMENT ON THE MONOGENITY OF A FAMILY OF TRINOMIALS
Diophantine Equations and Power Integral Bases
Newton polygons of higher order in algebraic number theory
Sur les polynômes à coefficients entiérs et de discriminant donné
On index divisors and monogenity of certain septic number fields defined by x⁷ + ax³ + b
On the index of the octic number field defined by \(x^8 + ax + b\)
On nonmonogenic number fields defined by trinomials of type \(x^n +ax^m+b\)

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