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New posts in principal-ideal-domains
Quotient of polynomials, PID but not Euclidean domain?
abstract-algebra
reference-request
commutative-algebra
principal-ideal-domains
$R/Ra$ is an injective module over itself
abstract-algebra
modules
principal-ideal-domains
injective-module
When is $\Bbb{Z[\zeta_n]}$ a PID?
ring-theory
principal-ideal-domains
Prime elements in $\mathbb{Z}[\sqrt{2}]$
abstract-algebra
ring-theory
principal-ideal-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
Euler's remarkable prime-producing polynomial and quadratic UFDs
abstract-algebra
prime-numbers
algebraic-number-theory
principal-ideal-domains
Prove that a UFD is a PID if and only if every nonzero prime ideal is maximal
abstract-algebra
principal-ideal-domains
unique-factorization-domains
How does a Class group measure the failure of Unique factorization?
number-theory
algebraic-number-theory
ideals
principal-ideal-domains
class-field-theory
$\mathbb Z\times\mathbb Z$ is principal but is not a PID
abstract-algebra
ring-theory
ideals
principal-ideal-domains
Norm-Euclidean rings?
abstract-algebra
number-theory
ring-theory
algebraic-number-theory
principal-ideal-domains
Non-principal ideal in $K[x,y]$? [duplicate]
abstract-algebra
ring-theory
field-theory
principal-ideal-domains
Why is $(2, 1+\sqrt{-5})$ not principal?
abstract-algebra
ideals
principal-ideal-domains
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
abstract-algebra
ring-theory
ideals
principal-ideal-domains
Greatest common divisor in the Gaussian Integers
abstract-algebra
principal-ideal-domains
Prove that $n^2+n+41$ is prime for $n<40$
abstract-algebra
elementary-number-theory
prime-numbers
principal-ideal-domains
An integral domain whose every prime ideal is principal is a PID
abstract-algebra
commutative-algebra
ideals
principal-ideal-domains
Ring of integers is a PID but not a Euclidean domain
abstract-algebra
algebraic-number-theory
principal-ideal-domains
unique-factorization-domains
Is the localization of a PID a PID?
abstract-algebra
commutative-algebra
principal-ideal-domains
localization
The ring $\Bbb Z\left [\frac{-1+\sqrt{-19}}{2}\right ]$ is not a Euclidean domain
abstract-algebra
ring-theory
principal-ideal-domains
euclidean-domain
A subring of the field of fractions of a PID is a PID as well.
abstract-algebra
commutative-algebra
ring-theory
principal-ideal-domains
integral-domain
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