New posts in commutative-algebra

Localization - the equivalence ratio and subrings.

Unramified primes of splitting field

$k[x]/(x^n)$ module with finite free resolution is free

Is an ideal finitely generated if its radical is finitely generated?

Is the image of a tensor product equal to the tensor product of the images?

Is it really necessary to work with the fraction field here?

Do the zero divisors form an ideal?

If $A[[x]]$ is Noetherian, will $A$ be Noetherian?

Help understand canonical isomorphism in localization (tensor products)

A formula for the radical of $\mathbb{Z}/n\mathbb{Z}$.

Origin of the modern definition of the tensor product

Generators of the ideal correspond to $d$-uple embedding

Question about proof of $A[X] \otimes_A A[Y] \cong A[X, Y] $

Every module over a field is free. Is every commutative ring whose modules are all free a field?

Prove that $\mathbb{C}[x,y] \ncong \mathbb{C}[x]\oplus\mathbb{C}[y]$

Coordinate rings in projective spaces. What are they?

The fibers of a finite morphism of affine varieties are all finite

Basic exercise on localization of modules

Injectivity of $I\leadsto V_I(-)$ and relation to Hilbert's Nullstellensatz

Commutative rings without assuming identity