New posts in commutative-algebra

Does there exist a projective module over $k[x_1,...,x_n]$ which is not free?

When is the tensor product of rings of integers again a ring of integers?

Injective Modules Motivation & Intuition

When some polynomials in $\mathbb Z[X]$ determine a regular sequence in $\mathbb Z[X_1,\dots,X_n]$?

In a reduced ring the set of zero divisors equals the union of minimal prime ideals.

Contents of Tor modules

Why is the (-1)-th coefficient of $f^n f'$ equal to 0, without dividing by $n+1$?

Help needed in understanding this proof of localization

Intuition for when modules are flat

Proof that a domain is normal (2)

Does the following property of the direct limit of a direct system follow from the axioms for a direct limit?

Associate prime ideals and exact sequences of $R$-modules

Maximal ideals in polynomial rings over a field

Rings in which every ideal contains a minimal ideal

Example that inverse limit is not exact

Ideal correspondence

Length of maximal chain of prime ideals equals transcendence degree of fraction field?

Koszul complex of locally free sheaves

Intersection of powers of maximal ideals

When is a field a nontrivial field of fractions?