One of the classical problems in algebraic number theory, going back among others to
Dedekind [De78], Hensel [He08], and Hasse [Ha63], is to decide if an algebraic number field …

Monogenity is a classical area of algebraic number theory that continues to be actively
researched. This paper collects the results obtained over the past few years in this area …

Discriminant equations are an important class of Diophantine equations with close ties to
algebraic number theory, Diophantine approximation and Diophantine geometry. This book …

Let K= Q (α) be a number field generated by a complex root α of a monic irreducible
trinomial F (x)= x 6+ ax 3+ b∈ Z [x]. There are extensive literature of monogenity of number …

We present efficient algorithms for solving Legendre equations over $\mathbb Q
$(equivalently, for finding rational points on rational conics) and parametrizing all solutions …

Abstract top The problem of determining power integral bases in algebraic number fields is
equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]) …

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 problem …

Let m be a square-free integer, m≡2,3\pmod4. We show that the number field
K=Q(i,\sqrt4m) is non-monogene, that is, it does not admit any power integral bases of type …

Monogenity of pure fields is recently intensively investigated. There are several papers on
conditions for the monogenity and non-monogenity of pure fields of various degrees …

J. Harrington and L. Jones characterized monogenity of four new parametric families of
quartic polynomials with various Galois groups. In this note we intend to describe all …