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New posts in unique-factorization-domains
Ring of formal power series over a principal ideal domain is a unique factorisation domain
abstract-algebra
ring-theory
principal-ideal-domains
noetherian
unique-factorization-domains
Given $d \equiv 5 \pmod {10}$, prove $\mathcal{O}_{\mathbb{Q}(\sqrt{d})}$ never has unique factorization
algebraic-number-theory
class-field-theory
unique-factorization-domains
$\textbf Z[\sqrt{pq}]$ is not a UFD if $\left( \frac{q}p \right) = -1$ and $p \equiv 1 \pmod 4$. [duplicate]
abstract-algebra
ring-theory
algebraic-number-theory
unique-factorization-domains
For which $d \in \mathbb{Z}$ is $\mathbb{Z}[\sqrt{d}]$ a unique factorization domain?
abstract-algebra
ring-theory
unique-factorization-domains
How to determine which classes of integral domains a quadratic integer ring is in? [duplicate]
ring-theory
algebraic-number-theory
principal-ideal-domains
unique-factorization-domains
When irreducible elements of a UFD remain irreducible in a ring extension
abstract-algebra
algebraic-geometry
ring-theory
commutative-algebra
unique-factorization-domains
Defining irreducible polynomials over polynomial rings
abstract-algebra
unique-factorization-domains
polynomial-rings
What is the correct notion of unique factorization in a ring?
abstract-algebra
ring-theory
prime-factorization
unique-factorization-domains
An example of a non Noetherian UFD
abstract-algebra
ring-theory
unique-factorization-domains
Example of a domain where all irreducibles are primes and that is not a GCD domain
ring-theory
divisibility
principal-ideal-domains
unique-factorization-domains
Is there an Integral domain that is a GCD domain but NOT a UFD? [duplicate]
commutative-algebra
divisibility
integral-domain
unique-factorization-domains
gcd-and-lcm
Is the coordinate ring of SL2 a UFD?
abstract-algebra
ring-theory
commutative-algebra
unique-factorization-domains
When is $\mathbb{Z}[\sqrt{d}]$ not an UFD (for $d>1$)?
ring-theory
algebraic-number-theory
unique-factorization-domains
Definition of UFD and the fact that UFDs are integrally closed
abstract-algebra
ring-theory
prime-factorization
unique-factorization-domains
Does UFD imply noetherian?
commutative-algebra
unique-factorization-domains
Looking for an example of a GCD domain which is not a UFD
commutative-algebra
divisibility
integral-domain
unique-factorization-domains
gcd-and-lcm
A case where a UFD is a PID
abstract-algebra
ring-theory
principal-ideal-domains
unique-factorization-domains
Why is the ring of holomorphic functions not a UFD?
complex-analysis
commutative-algebra
unique-factorization-domains
For which values of $d<0$ , is the subring of quadratic integers of $\mathbb Q[\sqrt{d}]$ is a PID?
ring-theory
algebraic-number-theory
principal-ideal-domains
unique-factorization-domains
$A=\frac{\mathbb{C}[X,Y]}{(X^2+Y^2-1)}$ is a PID.
ring-theory
commutative-algebra
principal-ideal-domains
unique-factorization-domains
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