Newbetuts

When does $V/\operatorname{ker}(\phi)\simeq\phi(V)$ imply $V\simeq\operatorname{ker}(\phi)\oplus\phi(V)$?

If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units

Are distinct prime ideals in a ring always coprime? If not, then when are they?

For which $d<0$ is $\mathbb Z[\sqrt{d}]$ an Euclidean Domain? [duplicate]

$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?

When is a product of two ideals strictly included in their intersection?

Proof that in an integral domain every prime element is irreducible [duplicate]

What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

uncertain orthogonality of discrete Fourier transform on the ring of integers modulo some number

Existence of non-commutative ordered ring

Is any UFD also a PID?

Does any integral domain contain an irreducible element?

Euclidean domain $\mathbb{Z}[\sqrt{d}]$ [duplicate]

Prove: The pre-image of an ideal is an ideal.

Proof that $\mathbb Z[\sqrt{3}]$ is a Euclidean Domain

Maximal Ideals in Ring of Continuous Functions

New posts in ring-theory

When does $V/\operatorname{ker}(\phi)\simeq\phi(V)$ imply $V\simeq\operatorname{ker}(\phi)\oplus\phi(V)$?

Is it possible to define a ring as a category?

equivalent characterizations of discrete valuation rings

Class of rings between fields and euclidean domains (improvement of euclideanity)

An ideal that is radical but not prime.

If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units

Are distinct prime ideals in a ring always coprime? If not, then when are they?

For which $d<0$ is $\mathbb Z[\sqrt{d}]$ an Euclidean Domain? [duplicate]

$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?

When is a product of two ideals strictly included in their intersection?

Proof that in an integral domain every prime element is irreducible [duplicate]

What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?

uncertain orthogonality of discrete Fourier transform on the ring of integers modulo some number

Existence of non-commutative ordered ring

Is any UFD also a PID?

Does any integral domain contain an irreducible element?

Euclidean domain $\mathbb{Z}[\sqrt{d}]$ [duplicate]

Prove: The pre-image of an ideal is an ideal.

Proof that $\mathbb Z[\sqrt{3}]$ is a Euclidean Domain

Maximal Ideals in Ring of Continuous Functions