Newbetuts

Looking for a special class of ideals such that If every ascending chain of ideals from this class stabilizes, then $R$ is a Noetherian ring.

Is there an algebraic non-rational extension of the integers, whose set of prime elements contains the prime integers?

Intuition for ideal quotient / colon ideal?

Minimal spectrum of a commutative ring

Multidimensional Hensel lifting

Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?

diagonalizing a matrix over the $\ell$-adics

When does tensor product have a (exact) left adjoint?

Quotient of a local ring at a point is a finite dimensional vector space

The set of zero divisors is a prime ideal

Checking if given polynomials are units in $\mathbb{Z}_7[x]$ [duplicate]

Milnor's exercise: for any manifold $M$, $\mathrm{Hom}(C^\infty(M,\mathbb{R}),\mathbb{R})\cong M$

Counter Example for Going Down Theorem

Coordinate ring of the unit circle is never a UFD?

Integral extensions: one prime lying over implies equal localization

New posts in commutative-algebra

Looking for a special class of ideals such that If every ascending chain of ideals from this class stabilizes, then $R$ is a Noetherian ring.

Can every irreducible cubic be proved irreducible using the Eisenstein criterion?

Prove that the given polynomial is irreducible in $\mathbb{Z}[X]$.

Grade of a maximal prime ideal in a Noetherian UFD

When is the pushforward / direct image of a reflexive sheaf locally free?

Why is the topology on $\operatorname{Proj} B$ induced from that on $\operatorname{Spec}(B)?$

Is there an algebraic non-rational extension of the integers, whose set of prime elements contains the prime integers?

Intuition for ideal quotient / colon ideal?

Minimal spectrum of a commutative ring

Multidimensional Hensel lifting

Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?

diagonalizing a matrix over the $\ell$-adics

When does tensor product have a (exact) left adjoint?

Quotient of a local ring at a point is a finite dimensional vector space

The set of zero divisors is a prime ideal

Checking if given polynomials are units in $\mathbb{Z}_7[x]$ [duplicate]

Milnor's exercise: for any manifold $M$, $\mathrm{Hom}(C^\infty(M,\mathbb{R}),\mathbb{R})\cong M$

Counter Example for Going Down Theorem

Coordinate ring of the unit circle is never a UFD?

Integral extensions: one prime lying over implies equal localization