New posts in Commutative Algebra

How to show $k[x]$ is not isomorphic to $k[x,y]/(xy+x^3+y^3)$?

Every $2$-dimensional commutative $k$-algebra with only one prime ideal is isomorphic to $k[x]/(x^2)$

$K$-valued functions on an infinite set

Are projective modules over $\mathbb{Z}[x_1,...,x_m]$ free?

Why do we need prime ideals in the spectrum of a ring?

If $R$ is a reduced Noetherian ring, then every prime ideal in the total quotient ring $K(R)$ is maximal.

Definition of isomorphism of graded rings

Ext and Tor duality

Example of the non-commutative ring with the set of units are commutative

Invertibility of elements in $A[x]$ with coefficients in the Jacobson radical