New posts in principal-ideal-domains

$\mathbb{Q}(\sqrt[3]{17})$ has class number $1$

algebraic-number-theory principal-ideal-domains ramification ideal-class-group

Why is the polynomial ring of more than one variable not a PID?

polynomials ring-theory principal-ideal-domains

gcd in principal ideal domain

abstract-algebra ring-theory principal-ideal-domains

Prove that $M$ is a free module if and only if $M$ is a projective module over $PID$.

abstract-algebra ring-theory modules principal-ideal-domains projective-module

Principal ideal rings that are not integral domains

abstract-algebra ring-theory principal-ideal-domains integral-domain

Why define vector spaces over fields instead of a PID?

ring-theory vector-spaces principal-ideal-domains

Proof for maximal ideals in $\mathbb{Z}[x]$ [duplicate]

abstract-algebra ring-theory ideals factoring principal-ideal-domains

Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID

number-theory algebraic-number-theory principal-ideal-domains

$R/Rg$ is a field iff $g\in R$ is irreducible.

abstract-algebra ring-theory principal-ideal-domains

Proving a prime ideal is maximal in a PID

abstract-algebra ring-theory maximal-and-prime-ideals principal-ideal-domains

Rings of integers of number field and free modules over a PID

number-theory principal-ideal-domains free-modules

If $F$ is a field, then $F[x]$ is a principal ideal domain proof question

abstract-algebra polynomials proof-explanation principal-ideal-domains

Structure theorem (PIDs) from Smith Normal Form

abstract-algebra modules principal-ideal-domains smith-normal-form

Finitely generated modules over PID

abstract-algebra modules principal-ideal-domains

Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.

abstract-algebra ring-theory principal-ideal-domains

$R$ is PID, so $R/I$ is PID, and application on $\mathbb{Z}$ and $\mathbb{N}$

abstract-algebra ring-theory principal-ideal-domains

Is any UFD also a PID?

abstract-algebra commutative-algebra ring-theory principal-ideal-domains unique-factorization-domains

Proofs of the structure theorem for finitely generated modules over a PID

abstract-algebra modules principal-ideal-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

Does there exist a ring which is not a principal ideal ring and which has exactly six different ideals?

abstract-algebra ring-theory ideals examples-counterexamples principal-ideal-domains