On monogenity of certain pure number fields defined by xpr − m
Hamid Ben Yakkou, Lhoussain El Fadil
Abstract
Let [Formula: see text] be a pure number field generated by a complex root [Formula: see text] of a monic irreducible polynomial [Formula: see text] where [Formula: see text] is a square free rational integer, [Formula: see text] is a rational prime integer, and [Formula: see text] is a positive integer. In this paper, we study the monogenity of [Formula: see text]. We prove that if [Formula: see text], then [Formula: see text] is monogenic. But if [Formula: see text] and [Formula: see text], then [Formula: see text] is not monogenic. Some illustrating examples are given.
Topics & Concepts
MathematicsInteger (computer science)CombinatoricsMonic polynomialPrime (order theory)Field (mathematics)Rational numberPolynomialPure mathematicsComputer scienceMathematical analysisProgramming languageAlgebraic Geometry and Number TheoryAnalytic Number Theory ResearchCoding theory and cryptography