68 citations · 107 across the 12 of their papers we have counts for
14 papers
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…
Totally real Thue inequalities over imaginary quadratic fields
István Gaál, Borka Jadrijević, László Remete
Let be an irreducible binary form of degree with integer coefficients and with real roots. Let be an imaginary quadratic field, with ring of integers . L…
Solving binomial Thue equations
István Gaál, László Remete
We consider binomial Thue equations of type in . Optimizing the method of Peth\H o we perform an extensive calculation by a high performance computer to…
Binomial Thue equations and power integral bases in pure quartic fields
István Gaál, László Remete
It is a classical problem in algebraic number theory to decide if a number field admits power integral bases and further to calculate all generators of power integral bases. This p…
Relative power integral bases in infinite families of quartic extensions of quadratic fields
István Gaál, Tí mea Szabó
We consider infinite parametric families of octic fields, that are quartic extensions of quadratic fields. We describe all relative power integral bases of the octic fields over th…
Non-monogenity in a family of octic fields
István Gaál, László Remete
Let be a square-free positive integer, . We show that the number field is non-monogene, that is it does not admit any power in…
Calculating power integral bases by using relative power integral bases
István Gaál, László Remete, Tí mea Szabó
Let be number fields. We consider the relation of relative power integral bases of over with absolute power integral bases of over . We show how generat…
Integral bases and monogenity of pure fields
István Gaál, László Remete
Let be a square-free integer (). We show that the structure of the integral bases of the fields are periodic in . For we sh…
Integral bases and monogenity of the simplest sextic fields
István Gaál, László Remete
Let be an integer, such that is square free. Let be a root of \[ f=x^6-2mx^5-(5m+15)x^4-20x^3+5mx^2+(2m+6)x+1. \] The totally real cyclic field…