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On the monogenity of quartic number fields defined by
Lhoussain El Fadil, István Gaál
For any quartic number field generated by a root of an irreducible trinomial of type , we characterize when is integrally closed. Also for $p=2,3…
On integral bases and monogenity of pure octic number fields with non-square free parameters
Lhoussain El Fadil, István Gaál
In all available papers, on power integral bases of pure octic number fields , generated by a root of a monic irreducible polynomial , it was assu…
Monogenity in totally real extensions of imaginary quadratic fields with an application to simplest quartic fields
István Gaál
We describe an efficient algorithm to calculate generators of power integral bases in composites of totally real fields with imaginary quadratic fields. We show that the calculatio…
Totally real Thue inequalities over imaginary quadratic fields: an improvement
István Gaál, Borka Jadrijevic, László Remete
We significantly improve our results of Glas. Mat., III. Ser. 53(2018), No. 2, 229-238, reducing relative Thue inequalities to absolute ones.
Calculating "small" solutions of inhomogeneous relative Thue inequalities
István Gaál
Thue equations and their relative and inhomogeneous extensions are well known in the literature. There exist methods, usually tedious methods, for the complete resolution of these…
Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields
István Gaál, Borka Jadrijević, László Remete
The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known. The family of simplest cubic Thue equations was already s…