Results 31 to 40 of about 410 (42)

A generalization of a result on integers in metacyclic extensions

, 1999
J. E. Carter
semanticscholar   +1 more source

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Generating Infinite Families of Monogenic Polynomials Using a New Discriminant Formula

, 2020
Recently, Otake and Shaska have given a formula for the discriminant of quadrinomials of the form f(x) = xn + t(x2 + ax + b). In their concluding remarks, they ask if a formula can be found for the discriminant of f(x) = xn + tg(x) when n > deg(g) = 3 ...
L. Jones
semanticscholar   +1 more source

The monogeneity of radical extensions

Acta Arithmetica, 2021
Let L be a number field. We give necessary and sufficient conditions for a radical extension L ( n √ α) to be monogenic over L with n √ α as a generator, i.e., for n √ α to generate a power OL-basis for the ring of integers OL( n √ α).
Hanson Smith
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The use of infinity in pure number theory and algebra

International Journal of Algebra, 2019
What is meant here by pure number theory is elementary number theory from Fermat to Kronecker, what I call Fermat-Kronecker arithmetic, that is the method of infinite descent combined with the theory of forms or homogeneous polynomials which extends to ...
Y. Gauthier
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Euler's φ-function over the domain of Gaussian integers

Applied Mathematical Sciences, 2019
If n = d1d2...dk is a product of positive integer, then the φ-function is defined as φ(n) = (d1 − 1)(d2 − 1)...(dk − 1), which is considered as a generalization for Euler’s function whenever n is a product of distinct primes. In this paper, we extend the
Y. Awad, W. Zeid, H. Chehade
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Arithmetical Properties of Powers of Algebraic Numbers

, 2006
A. Dubickas
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The structure of the n-th roots of unity in residue rings of prime ideals P over p in algebraic number fields. Part IV: n-th roots of unity for general n

, 2017
Boaz Cohen
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The Structure of the n-th Roots of Unity in Residue Rings of Prime Ideals P over p in Algebraic Number Fields Part III: n-th Roots of Unity when n = p

, 2018
Boaz Cohen
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The Structure of the nth Roots of Unity in Residue Rings of Prime Ideals P over p in Algebraic Number Fields Part II : nth Roots of Unity when P ‖ ( p )

, 2017
Boaz Cohen
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ON SUBFIELDS OF A FIELD GENERATED BY TWO CONJUGATE ALGEBRAIC NUMBERS

Proceedings of the Edinburgh Mathematical Society, 2004
Paulius Drungilas, A. Dubickas
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