New posts in commutative-algebra

Is the quotient of a complete ring, complete?

Exercise with Nakayama's lemma

What is an example of a radical of sum of ideals not being equal to the sum of radicals?

Primes in a Power series ring

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

A question on faithfully flat extension

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

Proving a Certain $\mathbb{C}$-Algebra is a Domain Using a Specified Method

Algebraic vs. Integral Closure of a Ring

Vandermonde identity in a ring

Noetherian rings and prime ideals

How to show a ring is normal or not, and how to show the normalisation of the ring

Two definitions of Zariski Topology

Localizations of quotients of polynomial rings (2) and Zariski tangent space

Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?

Let $M$ be a maximal ideal in $R$ such that for all $x\in M$, $x+1$ is a unit. Show that $R$ is a local ring with maximal ideal $M$

Intuition behind Direct limits

What are the irreducible components of $V(xy-z^3,xz-y^3)$ in $\mathbb{A}^3_K$?

Tensor product of two finitely generated modules

The natural map $M \to M \otimes_R K$ is injective iff $M$ is torsion free