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New posts in commutative-algebra
Is the quotient of a complete ring, complete?
abstract-algebra
commutative-algebra
ring-theory
Exercise with Nakayama's lemma
abstract-algebra
commutative-algebra
modules
What is an example of a radical of sum of ideals not being equal to the sum of radicals?
commutative-algebra
Primes in a Power series ring
abstract-algebra
number-theory
commutative-algebra
ring-theory
Symmetric and exterior powers of a projective (flat) module are projective (flat)
commutative-algebra
ring-theory
modules
multilinear-algebra
exterior-algebra
A question on faithfully flat extension
commutative-algebra
Integral extensions of rings, when one of the rings is a field
abstract-algebra
commutative-algebra
ring-theory
examples-counterexamples
Proving a Certain $\mathbb{C}$-Algebra is a Domain Using a Specified Method
abstract-algebra
commutative-algebra
integral-domain
unique-factorization-domains
Algebraic vs. Integral Closure of a Ring
commutative-algebra
integral-dependence
Vandermonde identity in a ring
abstract-algebra
commutative-algebra
polynomials
ring-theory
binomial-coefficients
Noetherian rings and prime ideals
commutative-algebra
noetherian
How to show a ring is normal or not, and how to show the normalisation of the ring
commutative-algebra
Two definitions of Zariski Topology
algebraic-geometry
commutative-algebra
Localizations of quotients of polynomial rings (2) and Zariski tangent space
algebraic-geometry
commutative-algebra
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
abstract-algebra
commutative-algebra
definition
ideals
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 $M$
abstract-algebra
commutative-algebra
Intuition behind Direct limits
abstract-algebra
commutative-algebra
homological-algebra
What are the irreducible components of $V(xy-z^3,xz-y^3)$ in $\mathbb{A}^3_K$?
algebraic-geometry
commutative-algebra
Tensor product of two finitely generated modules
abstract-algebra
commutative-algebra
modules
tensor-products
finitely-generated
The natural map $M \to M \otimes_R K$ is injective iff $M$ is torsion free
commutative-algebra
tensor-products
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