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Irreducible-polynomials
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If $x^p−x−c$ is irreducible in $F[x]$ then it has no root in the field.
August 1st, 2022
irreducible-polynomials
abstract-algebra
field-theory
Factor into a product of irreducible polynomials
August 1st, 2022
abstract-algebra
irreducible-polynomials
field-theory
polynomials
Prove that the following cubic polynomial is irreducible over $\mathbb Q$
September 12th, 2021
polynomials
irreducible-polynomials
abstract-algebra
Multiplicative Inverse in a $256$ Galois Field
January 27th, 2020
polynomials
irreducible-polynomials
finite-fields
galois-theory
Proving some polynomials are irreducible using Eisenstein's criterion
August 1st, 2022
abstract-algebra
irreducible-polynomials
factoring
ring-theory
polynomials
What are the irreducible elements in $\mathbb{R}[x]$ and $\mathbb{C}[x]$?
August 1st, 2022
polynomials
abstract-algebra
irreducible-polynomials
Irreducible polynomials in Z[X]
August 1st, 2022
abstract-algebra
quadratics
irreducible-polynomials
Writing a polynomial as a product of irreducible polynomials over another field
August 1st, 2022
irreducible-polynomials
complex-numbers
field-theory
factoring
If a and b are odd integers then find the number of integral roots of $(x^{10} +ax^9 +b=0)$
August 1st, 2022
irreducible-polynomials
polynomials
Irreducible Polynomial over the Rationals
April 8th, 2020
irreducible-polynomials
polynomials
If f and g are irreducible polynomials in K[X,Y ] that are not associates, show that the zero set Z(f,g) is either empty or finite
February 3rd, 2020
polynomials
abstract-algebra
irreducible-polynomials
ring-theory
algebraic-geometry
Does irreducibility in $\mathbb Q[X]$ always imply the irreducibility in $\mathbb Z[X]$?
October 12th, 2020
polynomials
irreducible-polynomials
abstract-algebra
Irreducibility of a polynomial with degree $4$
August 1st, 2022
abstract-algebra
irreducible-polynomials
polynomials
field-theory
Prime ideals in $F[x]$ when $F$ is a field
August 1st, 2022
field-theory
irreducible-polynomials
$x^{p-1} + ... + x^2 + x + 1$ is irreducible using Eisenstein's criterion?
December 2nd, 2020
irreducible-polynomials
abstract-algebra
polynomials
ring-theory
Eisenstein criterion's condition
August 1st, 2022
irreducible-polynomials
polynomials
Irreducible Polynomials over $\mathbb{R}$ or $\mathbb{Q}$
August 1st, 2022
irreducible-polynomials
polynomials
The union of finite field extensions is a finite field extension
November 27th, 2020
irreducible-polynomials
extension-field
field-theory
abstract-algebra
Construction of addition and multiplication table for GF(4)
May 26th, 2020
irreducible-polynomials
finite-fields
Understanding calculations of log/antilog tables of polynomials over finite field
October 13th, 2020
irreducible-polynomials
finite-fields
logarithms
galois-theory
Roots of polynomials of the form $x^q-x-\alpha$ over $\mathbb F_{q^m}$
December 6th, 2020
irreducible-polynomials
polynomials
finite-fields
How to check if a polynomial in $F[x]$ is irreducible or not, for $F$ a finite field
November 3rd, 2020
abstract-algebra
irreducible-polynomials
polynomials
If $F$ is a subfield of an algebraically closed field $K$, then the algebraic closure $\overline{F}$ of $F$ in $K$ is also algebraically closed.
August 1st, 2022
abstract-algebra
irreducible-polynomials
extension-field
field-theory
$X^3-X-1$ irreducible in $\mathbb{Q}[X]$
February 15th, 2020
irreducible-polynomials
abstract-algebra
ring-theory
Prime elements and irreducible elements of quotient rings of polynomial ring
August 1st, 2022
abstract-algebra
irreducible-polynomials
polynomials
SAGE: Is it possible to extract the irreducible factor of a polynomial for the purpose of constructing a Number Field?
September 28th, 2020
sagemath
polynomials
irreducible-polynomials
Showing that $x^p - a$ either splits or is irreducible for characteristic $p$ (prime) in a field F.
August 1st, 2022
splitting-field
irreducible-polynomials
abstract-algebra
roots of polynomial over finite field
March 31st, 2020
roots
finite-fields
irreducible-polynomials
'shifted' polynomial preserves validity of Eisenstein irreducibility criterion of original, in finite fields?
August 1st, 2022
polynomials
irreducible-polynomials
finite-fields
Factor irreducible polynomial in Z[x] and R[x]
August 1st, 2022
factoring
extension-field
abstract-algebra
irreducible-polynomials
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