2021
DOI: 10.1142/s1793042121500858
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On monogenity of certain pure number fields defined by xpr − m

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: se… Show more

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Cited by 23 publications
(15 citation statements)
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“…This problem has been widely studied and of interest to several mathematicians (cf. [1], [2], [4], [5], [6], [7], [8], [10], [11]). Let K be an algebraic number field generated by a complex root θ of a monic irreducible polynomial f (x) having degree n with coefficients from the ring Z of integers.…”
Section: Introductionmentioning
confidence: 99%
“…This problem has been widely studied and of interest to several mathematicians (cf. [1], [2], [4], [5], [6], [7], [8], [10], [11]). Let K be an algebraic number field generated by a complex root θ of a monic irreducible polynomial f (x) having degree n with coefficients from the ring Z of integers.…”
Section: Introductionmentioning
confidence: 99%
“…Let K be a pure number field generated by a complex root α of a monic irreducible polynomial F (x) = x 3 r •7 s − m with m = ∓1 a square free integer, and r and s two positive integers. The case r = 0 or s = 0 has been studied in [4].…”
Section: Resultsmentioning
confidence: 99%
“…In [10,13,12,9,4,3,11], based on Newton polygon techniques, we studied the monogeneity of the pure number fields of degrees in the following list: 12, 18, 24, 36, p r , 3 k • 5 r , and 2 • 3 k . In this paper, based on Newton polygon techniques, we study the monogeneity of any pure number field K = Q(α) generated by a complex root of a monic irreducible polynomial F (x) = x 3 r •7 s − m, where m = ±1 is a square free integer, and r and s are positive integers.…”
mentioning
confidence: 99%
“…In [14], Gaál and Remete studied the monogenity of pure number fields K = Q( n √ m) for 3 ≤ n ≤ 9 and any square-free rational integer m = ±1. They also showed in [16] that if m ≡ 2 or 3 (mod 4) is a square-free rational integer, then the octic field K = Q(i, 4 √ m) is not monogenic. In [25],…”
Section: Introductionmentioning
confidence: 99%