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Arithmetic structure including both unique factorization and Dedekind domains
abstract-algebra
ring-theory
integral-domain
unique-factorization-domains
dedekind-domain
A quotient $\mathcal{O}/\mathfrak{a}$ of a Dedekind domain is principal (Neukirch exer 1.3.5)
commutative-algebra
algebraic-number-theory
ideals
dedekind-domain
An example of prime ideal $P$ in an integral domain such that $\bigcap_{n=1}^{\infty}P^n$ is not prime
abstract-algebra
ring-theory
commutative-algebra
maximal-and-prime-ideals
dedekind-domain
When is the tensor product of rings of integers again a ring of integers?
commutative-algebra
algebraic-number-theory
tensor-products
dedekind-domain
integer-rings
How does passing to ideals solve the problem of unique factorization?
number-theory
algebraic-number-theory
dedekind-domain
Torsion module Finite composition length
modules
dedekind-domain
If $A$ is a Dedekind domain and $I \subset A$ a non-zero ideal, then every ideal of $A/I$ is principal.
commutative-algebra
dedekind-domain
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
abstract-algebra
ring-theory
commutative-algebra
dedekind-domain
Dedekind domain with a finite number of prime ideals is principal
abstract-algebra
ring-theory
commutative-algebra
principal-ideal-domains
dedekind-domain
In a Dedekind domain every ideal is either principal or generated by two elements.
abstract-algebra
commutative-algebra
algebraic-number-theory
dedekind-domain
One-dimensional [Noetherian] UFD is a PID
reference-request
commutative-algebra
principal-ideal-domains
unique-factorization-domains
dedekind-domain
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