Results 71 to 80 of about 561 (135)
J. Harrington and L. Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later P. Voutier added a cyclic family.
Gaál, István
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Iterates of Quadratics and Monogenicity
We investigate monogenicity and prime splitting in extensions generated by roots of iterated quadratic polynomials. Let $f(x)\in\mathbb{Z}[x]$ be an irreducible, monic, quadratic polynomial, and write $f^n(x)$ for the $n^{\text{th}}$ iterate.
Smith, Hanson, Wolske, Zack
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Algebraic, Analytic, and Computational Number Theory and Its Applications [PDF]
Acciaro, Vincenzo +3 more
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On Index and Monogenity of Certain Number Fields Defined by Trinomials
Mathematica Slovaca, 2023Let K be a number field generated by a root θ of a monic irreducible trinomial F(x)=xn+axm+b∈ℤ[x] . In this paper, we study the problem of monogenity of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic.
L. El Fadil
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On the index divisors and monogenity of number fields defined by x 5 + ax 3 + b
Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2023The main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz[24] for any quintic number field K generated by a complex root α of a monic irreducible trinomial F(x) = x 5 + ax 3 + b ∈ ℤ [x].
L. El Fadil
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On index divisors and non-monogenity of certain quintic number fields defined by x 5 + ax m + bx + c
Communications in Algebra, 2023In this article, we deal with the problem of monogenity of quintic number fields defined by monic irreducible quadrinomials with m = 2, 3, 4. We give sufficient conditions on a, b, c, and m so that the index of the field K is nontrivial and we evaluate ...
O. Kchit
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On non-monogenity of the number fields defined by certain quadrinomials
Communications in Algebra, 2023Let p be a rational prime. Let be an algebraic number field with θ a root of an irreducible quadrinomial with . In the present paper, we give some explicit conditions involving only and s for which K is non-monogenic. If q is a prime number of the form ,
A. Jakhar +2 more
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MONOGENITY OF THE COMPOSITION OF POLYNOMIALS
Bulletin of the Australian Mathematical SocietyOne of the important problems in algebraic number theory is to study the monogenity of number fields. Monogenic number fields arise from the roots of monogenic polynomials.
Surender Kumar
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On common index divisors and monogenity of certain number fields defined by x 5 + ax 2 + b
Communications in Algebra, 2022Let be a number field generated by a complex root α of a monic irreducible trinomial In this paper, for every prime integer p, we give necessary and sufficient conditions on a and b so that p is a common index divisor of K.
L. El Fadil
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