Results 91 to 100 of about 561 (135)

Monogenity of iterates of irreducible binomials

Communications in Algebra
One of the oldest problems of algebraic number theory is to find a method to determine if the ring of integers of a number field K is Z[θ] for some θ∈K; a field for which the answer to this question is affirmative is referred to as a monogenic field ...
Himanshu Sharma, R. Sarma, Shanta Laishram   +2 more
semanticscholar   +1 more source

On the Monogenity of Totally Complex Pure Octic Fields

Axioms
Let 0,1≠m∈Z and α=m8. According to the results of Gaál and El Fadil, α generates a power integral basis in K=Q(α), if and only if m is square-free and m≢1(mod4).
Istv'an Ga'al
semanticscholar   +1 more source

On monogenic primitives of monogenic functions

Complex Variables and Elliptic Equations, 2007
The theory of functions with values in Clifford algebras shows a lot of analogies to the complex function theory in the complex one-dimensional case. The class of holomorphic functions is now the set of null solutions of a generalized Cauchy–Riemann system, the class of monogenic functions. Analogously to the complex case one can define a derivative of
I. Cação, K. Gürlebeck
openaire   +1 more source

On the monogenity and Galois group of certain classes of polynomials

Mathematica Slovaca
We say a monic polynomial g(x) ∈ ℤ[x] of degree n is monogenic if g(x) is irreducible over ℚ and {1, θ, …, θn−1} is a basis for the ring ℤK of integers of number field K = ℚ(θ), where θ is a root of g(x). Let f(x)=xn+c∑i=1n(ax)n−i∈Z[x]andF(x)=xn+c∑i=1nai−
A. Jakhar, R. Kalwaniya, Prabhakar Yadav
semanticscholar   +1 more source

Quasi-monogenic Functions

Advances in Applied Clifford Algebras, 2018
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openaire   +2 more sources

Monogenity of the composition of certain polynomials

Acta Arithmetica
We call a monic irreducible polynomial f(x)∈Z[x] to be monogenic if Z[θ] is the ring of integers of the number field Q(θ) where θ is a root of f(x). Finding the ring of integers of a number field is an important problem in algebraic number theory.
Himanshu Sharma, R. Sarma
semanticscholar   +1 more source

Monogenity of composition of quadrinomials

Mathematica Slovaca
An irreducible monic polynomial f ( x ) ∈ Z [ x ] $f(x)\in \mathbb{Z}[x]$ is said to be monogenic if Z [ θ ] $\mathbb{Z}[\theta ]$ is the ring of integers of the number field Q ( θ ) $\mathbb{Q}(\theta )$ for a root θ of f(x).
Himanshu Sharma
semanticscholar   +1 more source

On the monogenity of polynomials with non-squarefree discriminants

Acta Arithmetica
In 2012, for any integer n≥2, Kedlaya constructed an infinite class of monic irreducible polynomials of degree n with integer coefficients having squarefree discriminants. Such polynomials are necessarily monogenic.
Rupam Barman, Anuj Narode, Vinay Wagh
semanticscholar   +1 more source

Monogenic hypertension.

Polski merkuriusz lekarski : organ Polskiego Towarzystwa Lekarskiego, 2022
Monogenic hypertension (MH) is a rare form of arterial hypertension (AH) in which a single gene mutation is responsible for developing the disease. This article discusses the pathogenesis, genetics, phenotype, and treatment of monogenic forms of AH. According to Guyton's hypothesis, mutations responsible for MH development most often lead to increased ...
Aleksandra, Ostrowska, Piotr, Skrzypczyk
openaire   +1 more source

Hypercomplex monogenic and areolar monogenic functions

2001
Let us consider a partial differential equation of higher order with real constant coefficients of the form \[ P(D_x,D_y) u=\left(\sum^n_{k=0} \alpha_k D_x^{n-k} D_y^k\right)u=0,\;\alpha_n=1. \] To this equation one can associate an associative and commutative algebra of order \(n\) over the real field with the basis \(\{1,g,g^2, \dots,g^{n-1 ...
ÇELİK, NİSA, ÇAĞLIYAN, MEHMET
openaire   +2 more sources