New posts in commutative-algebra

Are the rings $k[[t^3,t^4,t^5]]$ and $k[[t^4,t^5,t^6]]$ Gorenstein? (Matsumura, Exercise 18.8)

commutative-algebra cohen-macaulay gorenstein

Why is the Artin-Rees lemma used here?

algebraic-geometry commutative-algebra

Showing that $M$ is free module over $(O_K \otimes_{\mathbb{Z}_p}U)$

number-theory algebraic-geometry commutative-algebra p-adic-number-theory

Isomorphism of rings implies isomorphism of vector spaces?

linear-algebra abstract-algebra commutative-algebra ring-theory vector-spaces

Vakil 14.2.E: $\mathcal L \cong \mathcal O_X(\mathrm{div}(s))$ for $s$ a rational section.

algebraic-geometry commutative-algebra

Proof that a certain domain is a valuation ring

abstract-algebra commutative-algebra

$R/I$ is not Noetherian. Prove that $I$ is a prime ideal.

abstract-algebra commutative-algebra ring-theory

Why is $V^{\vee}\otimes W^{\vee}\longrightarrow (V\otimes W)^{\vee}$ always injective?

commutative-algebra modules tensor-products dual-spaces monomorphisms

Chinese remainder theorem as sheaf condition?

algebraic-geometry commutative-algebra chinese-remainder-theorem affine-schemes

Royal way to learn algorithmic / computational / computer algebra

algebraic-geometry polynomials commutative-algebra computational-mathematics computer-algebra-systems

$\operatorname{Supp}(M)=V(\operatorname{Ann}M)$ if $M$ is finitely generated

commutative-algebra

Proof of $M$ Noetherian if and only if all submodules are finitely generated

commutative-algebra modules

If A is noetherian, then Spec(A) is noetherian

abstract-algebra commutative-algebra ring-theory

Universal property of the completion of rings / modules

abstract-algebra commutative-algebra

Are minimal prime ideals in a graded ring graded?

algebraic-geometry commutative-algebra ring-theory graded-rings

Nilpotent elements in $\mathbb{Z}_n$

abstract-algebra ring-theory commutative-algebra

For a prime ideal $\def\p{\mathfrak{p}}\p\subset A$ and a ring map $A\to B$, what is $B_\p/\p B_\p$? Can $\mathfrak{p}$ be a prime ideal of $B$?

algebraic-geometry commutative-algebra

Question about the definition of the Jacobian ideal

algebraic-geometry commutative-algebra

A basis of a field extension contained in a subring

commutative-algebra field-theory extension-field

Integral Extension of a Jacobson Ring

algebraic-geometry commutative-algebra