List questions from ideals | MathQA

If $A\subset B$, $\mathfrak{p}$ be a prime of $A$, $x+\mathfrak{p}B$ is a unit, irreducible $f\in A[X]$ has $f(x)=0$, must $[X^0]f\notin\mathfrak{p}$?

Published on 01 Apr 2026 - 6:56

Commutative algebra: Irreducible components of $\operatorname{Spec}(A)$

Published on 25 Mar 2026 - 23:33

Does $\bigcap^{\infty}_{k=0} (I + (X^k)) = I$ hold in a ring of formal power series?

Published on 26 Mar 2026 - 17:53

Proof: $S = \{[2m]_{1000} : m = 0, 1, ... , 500\}$ is an Ideal of $R = \mathbb{Z}_{1000}$

Published on 21 Mar 2023 - 12:49

Measurable sets modulo null sets is a complete boolean algebra

Published on 02 Apr 2026 - 9:28

Question on proof that all subgroups of $\mathbb{Z}$ and $\mathbb{Z_n}$ are subrings (and ideals).

Published on 22 Mar 2023 - 20:46

Radical of the ideal $(x^2,y^2)$

Published on 24 Mar 2023 - 8:30

Proof that these ideals in an integral closure are principal

Published on 07 Apr 2026 - 16:08

why is a Lie algebra not nilpotent even if an ideal is nilpotent and algebra quotient by ideal is nilpotent

Published on 26 Mar 2026 - 11:17

if a homogeneous polynomial is the square of a polynomial modulo $x^2 + y^2 - 1$, is it also congruent to a sum of squares of homogeneous polynomials?

Published on 23 Feb 2026 - 10:06

All prime ideals of size less than the Minkowski bound being principal implies that the ring of integers is a PID

Published on 28 Mar 2023 - 12:52

Free ring on a semi ring

Published on 26 Mar 2026 - 14:17

Uniqueness of prime ideal

Published on 29 Mar 2023 - 6:17

Prime ideal on $C^\infty((-1, 1))$ that is properly contained in the prime ideal consisting of all functions whose derivatives are all $0$.

Published on 01 Apr 2026 - 6:55

Understanding what $I \cdot J$ means when $I$ and $J$ are ideals.

Published on 29 Mar 2023 - 13:50