Results 21 to 30 of about 21,598 (116)

On the Monogenity of Quartic Number Fields Defined by x⁴ + ax² + b

Mathematics
For any quartic number field K generated by a root α of an irreducible trinomial of type x4+ax2+b∈Z[x], we characterize when Z[α] is integrally closed. Also for p=2, 3, we explicitly give the highest power of p dividing i(K), the common index divisor of ...
Lhoussain El Fadil, István Gaál
doaj   +1 more source

Non-unique factorization of polynomials over residue class rings of the integers

, 2011
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic.
Anderson D. D., Christopher Frei, Frisch S., McDonald B. R., Sophie Frisch, Wan Z.-X.   +5 more
core   +1 more source

Genetics of polynomials over local fields

, 2014
Let $(K,v)$ be a discrete valued field with valuation ring $\oo$, and let $\oo_v$ be the completion of $\oo$ with respect to the $v$-adic topology. In this paper we discuss the advantages of manipulating polynomials in $\oo_v[x]$ in a computer by means ...
Guàrdia, Jordi, Nart, Enric
core   +1 more source

Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field [PDF]

, 2015
The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements.
Rezola, Nolberto
core  

Computing the bound of an Ore polynomial. Applications to factorization

, 2018
We develop a fast algorithm for computing the bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a factorization ...
Gomez-Torrecillas, Jose, Lobillo, F. J., Navarro, Gabriel   +2 more
core   +1 more source

A Homological Approach to Factorization [PDF]

, 2016
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D.
Coykendall, Jim, Goodell, Brandon
core  

The Factor Domains that Result from Uppers to Prime Ideals in Polynomial Rings [PDF]

Kyungpook mathematical journal, 2010
Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; L[X] a monic irreducible polynomial; any root of in F; and Q = >, the upper to P with respect to . Then R[X]/Q is R-algebra isomorphic to ; and is R-isomorphic to an overring of D if and only if deg() = 1.
openaire   +1 more source

Multiple Factorizations of Bivariate Linear Partial Differential Operators

, 2009
We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate LPDO has a first-order left and right factors such that their symbols are
A.V. Zhiber, C. Athorne, D. Grigoriev, D. Grigoriev, D. Grigoriev, E. Shemyakova, E. Shemyakova, E. Shemyakova, I. Anderson, I. Anderson, P. Cassidy, S. Tsarev, S. Tsarev, S.P. Tsarev, W. Sit, Z. Li, Z. Li   +16 more
core   +1 more source

First-degree prime ideals of composite extensions

Journal of Mathematical Cryptology
Let Q(α){\mathbb{Q}}\left(\alpha ) and Q(β){\mathbb{Q}}\left(\beta ) be linearly disjoint number fields and let Q(θ){\mathbb{Q}}\left(\theta ) be their compositum.
Santilli Giordano, Taufer Daniele
doaj   +1 more source

Factorization of Prime Ideal Extensions in Dedekind Domains

Journal of Symbolic Computation, 1995
The author describes a method of factorizing ideals in a finite separable extension of a Dedekind domain lying over a prime ideal of the base domain, as a product of prime ideals. She also discusses the computational aspects of the problem.
openaire   +2 more sources