Newbetuts

An example of prime ideal $P$ in an integral domain such that $\bigcap_{n=1}^{\infty}P^n$ is not prime

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

When does $f,g \in R[x]$ relatively prime imply $f,g \in R[[x]]$ relatively prime.

Are the notations $C[0,1]$ and $C([0,1])$ the same?

Injective Modules Motivation & Intuition

To find the nilpotent elements of $\Bbb Z_n$ and also the number of nilpotent elements of $\Bbb Z_n$.

Directly indecomposable rings

Real forms of complex vector spaces and $\mathbb{C}$-algebra

If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.

The jacobson radical of a ring $R$ contains no idempotents other than $0$. [closed]

Relation between semiring of sets and semiring in abstract algebra.

Question about all the homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

Result due to Cohn, unique division ring whose unit group is a given group?

Does this notion of morphism of noncommutative rings appear in the ring theory literature?

Perron polynomial irreducibility criterion

Is it really unknown that every endomorphism of the Weyl algebra $A_1$ is an isomorphism?

New posts in ring-theory

Ring with non-trivial idempotent splitting as product of two rings

Show that $\mathbb{C}[x,y]/(x^2+y^2-1)$ is a UFD. [duplicate]

Why do the Localization of a Ring

Maximal ideal space of $c_{\mathcal{U}}$

An example of prime ideal $P$ in an integral domain such that $\bigcap_{n=1}^{\infty}P^n$ is not prime

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

When does $f,g \in R[x]$ relatively prime imply $f,g \in R[[x]]$ relatively prime.

Are the notations $C[0,1]$ and $C([0,1])$ the same?

Injective Modules Motivation & Intuition

To find the nilpotent elements of $\Bbb Z_n$ and also the number of nilpotent elements of $\Bbb Z_n$.

Directly indecomposable rings

Real forms of complex vector spaces and $\mathbb{C}$-algebra

If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.

The jacobson radical of a ring $R$ contains no idempotents other than $0$. [closed]

Relation between semiring of sets and semiring in abstract algebra.

Question about all the homomorphisms from $\mathbb{Z}$ to $\mathbb{Z}$

Result due to Cohn, unique division ring whose unit group is a given group?

Does this notion of morphism of noncommutative rings appear in the ring theory literature?

Perron polynomial irreducibility criterion

Is it really unknown that every endomorphism of the Weyl algebra $A_1$ is an isomorphism?