New posts in ring-theory

Show the direct sum of noetherian R-modules is noetherian.

If A is noetherian, then Spec(A) is noetherian

Sum of ideals in a ring

Invertibility of elements in a left Noetherian ring

Are minimal prime ideals in a graded ring graded?

Nilpotent elements in $\mathbb{Z}_n$

For a field $K$, is there a way to prove that $K[x]$ is a PID without mentioning Euclidean domain?

Isomorphism of $S^1$.

Arithmetic structure including both unique factorization and Dedekind domains

To find all integers $n > 1$ for which $(n-1)!$ is a zero-divisor in $Z_n$.

Is the quotient of a complete ring, complete?

Primes in a Power series ring

Symmetric and exterior powers of a projective (flat) module are projective (flat)

Integral extensions of rings, when one of the rings is a field

Cosets modulo $(2+i)$ in $\mathbb{Z}[i]$

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

If a sub-C*-algebra does not contain the unit, is it contained in a proper ideal?

Does $f(x) \in \mathbb{Z}[x]$ irreducible, imply $f(2x)$ also irreducible?

Examples of non-Euclidean domains which have a universal side divisor

Characteristic of an integral domain must be either $0$ or a prime number.