Newbetuts
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New posts in ring-theory
Prove that $p$ is prime in $\mathbb{Z}[\sqrt{-3}]$ if and only if $x^2+3$ is irreducible in $\mathbb{F}_p[x]$.
abstract-algebra
ring-theory
Products of ideals is an ideal and comaximal ideals
abstract-algebra
ring-theory
ideals
For which monic irreducible $f(x)\in \mathbb Z[x]$ , is $f(x^2)$ also irreducible in $\mathbb Z[x]$?
polynomials
ring-theory
irreducible-polynomials
Checking if given polynomials are units in $\mathbb{Z}_7[x]$ [duplicate]
abstract-algebra
polynomials
ring-theory
commutative-algebra
why $\mathbb Z[\sqrt 2] \ncong \mathbb Z[\sqrt 3]$?
ring-theory
Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$?
abstract-algebra
ring-theory
proof-verification
quotient-spaces
Prove that $R[x]$ is an integral domain if and only if $R$ is an integral domain. [duplicate]
abstract-algebra
ring-theory
integral-domain
polynomial-rings
Importance of the Artin-Wedderburn theorem
ring-theory
self-learning
The Picard-Brauer short exact sequence
reference-request
commutative-algebra
ring-theory
Checking if $\langle 2 \rangle$ is a maximal ideal in $\mathbb{Z}[i]$
abstract-algebra
proof-verification
ring-theory
ideals
Prove that $\mathbb{Q}[\sqrt{2}]=a+b\sqrt{2}$ is isomorphic to $\mathbb{Q}[x]/(x^2-2)$.
abstract-algebra
ring-theory
group-isomorphism
Example of finite ring with a non principal ideal
abstract-algebra
ring-theory
finite-rings
Find all irreducible polynomials of degrees 1,2 and 4 over $\mathbb{F_2}$.
abstract-algebra
ring-theory
field-theory
Showing a Functor is not Representable
abstract-algebra
ring-theory
category-theory
prove $(n) \supseteq (m)\iff n\mid m\ $ (contains = divides for principal ideals)
elementary-number-theory
ring-theory
divisibility
ideals
Prove that $\Bbb Z[\sqrt{2}, \sqrt{3}]$ does not equal $\Bbb Z[\sqrt{2} + \sqrt{3}]$. [duplicate]
abstract-algebra
ring-theory
Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)
abstract-algebra
ring-theory
finite-groups
representation-theory
group-rings
Is this ring Noetherian?
commutative-algebra
ring-theory
noetherian
When is the map $x\rightarrow x^k$ injective in $\mathbb Z_n$?
ring-theory
modular-arithmetic
On the cubic generalization $(a^3+b^3+c^3+d^3)(e^3+f^3+g^3+h^3 ) = v_1^3+v_2^3+v_3^3+v_4^3$ for the Euler four-square
number-theory
polynomials
ring-theory
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