I’m so wired attacking reducibility using the fact that I’m on a field and playing with orders of elements to show there is no linear or quadratic factors. But $\mathbb{Z}$ is not a field and the multi variable part of it is confusing. Any hints are appreciated!
2026-03-25 04:58:48.1774414728
How to prove $x^5 + y^7 +11$ irreducible in $\mathbb{Z}[x,y]$
141 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in RING-THEORY
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- A commutative ring is prime if and only if it is a domain.
- Find gcd and invertible elements of a ring.
- Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain.
- Prove that $Z[i]/(5)$ is not a field. Check proof?
- If $P$ is a prime ideal of $R[x;\delta]$ such as $P\cap R=\{0\}$, is $P(Q[x;\delta])$ also prime?
- Let $R$ be a simple ring having a minimal left ideal $L$. Then every simple $R$-module is isomorphic to $L$.
- A quotient of a polynomial ring
- Does a ring isomorphism between two $F$-algebras must be a $F$-linear transformation
- Prove that a ring of fractions is a local ring
Related Questions in IRREDUCIBLE-POLYNOMIALS
- $x^{2}(x−1)^{2}(x^2+1)+y^2$ is irreducible over $\mathbb{C}[x,y].$
- Is the following polynomial irreductible over $\mathbb{Z}[X]$?
- Does irreducibility in $\mathbb{F}_p[x]$ imply irreducibility in $\mathbb{Q}[x]$?
- discriminant and irreducibility of $x^p - (p+1)x - 1$
- galois group of irreducible monic cubic polynomial
- When will $F[x]/\langle p(x)\rangle$ strictly contain $F$?
- On reducibility over $\mathbb{Z}$ of a special class of polynomials .
- Eisenstein's criterion over polynomials irreducible
- Optimal normal basis in Tower field construction
- If $f$ has $\deg(f)$ distince roots whose order are the same, then is $f$ irreducible?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?