Intereting Posts

Proving $\int_{0}^{\pi/2}x\sqrt{\tan{x}}\log{\sin{x}}\,\mathrm dx=-\frac{\pi\sqrt{2}}{48}(\pi^2+12\pi \log{2}+24\log^2{2}) $
Infinite sum of reciprocals of pentagonal numbers
Pure algebra: Show that this expression is positive
Smoothness of Fourier transform of $\frac{1}{|x|^p}$
Unclear on why Meissel's approach to counting primes works
When Are We Allowed to Break Up A Triple Integral?
Bhattacharya Distance (or A Measure of Similarity) — On Matrices with Different Dimensions
Prove every element of $G$ has finite order.
How prove that $q \geq b+d$ for $ad-bc = 1$ and $\frac{a}{b} > \frac{p}{q} > \frac{c}{d}$?
Conjecture: Only one Fibonacci number is the sum of two cubes
Coefficients of a polynomial also are the roots of the polynomial?
Polynomial whose only values are squares
Show that $C_0(, \mathbb{R})$ is not $\sigma$-compact
Minimum Modulus Principle for a constant fuction in a simple closed curve
Finding sine of an angle in degrees without $\pi$

Suppose $A$ is a local domain, with field of fractions $K$, let $A’$ be the integral closure of $A$ in $K$, is $A’$ a local ring?

- Is quotient of a ring by a power of a maximal ideal local?
- Verifying Hilberts Nullstellensatz on a particular example
- A proof using Yoneda lemma
- $\mathfrak{a}(M/N) = (\alpha M + N) / N$
- Is an irreducible ideal in $R$ irreducible in $R$?
- Proposition 5.21 in Atiyah-MacDonald
- Semilocal commutative ring with two or three maximal ideals
- If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?
- Is this quotient ring $\mathbb{C}/\ker\phi$ integrally closed?
- Is there a domain which is not UFD but has a maximal principal ideal?

Not necessarily. E.g. consider $A = \mathbb Z_{(5)} + 5 \mathbb Z_{(5)}[i]$. (Here $\mathbb Z_{(5)}$ denotes $\mathbb Z$ localized at the prime ideal $(5)$.)

Then $A’ = \mathbb Z_{(5)}[i],$ which has two maximal ideals (the ideals generated by $2 \pm i$).

For a geometric example, consider the local ring at the node of the nodal cubic

$y^2 = x^2(x +1).$

- Field of sets versus a field as an algebraic structure
- Formula for Combinations With Replacement
- Does this packing problem even have an optimal solution?
- Distinguishable painted prisms with six colors (repetition allowed)
- What's the difference between early transcendentals and late transcendentals?
- Sum of two periodic functions
- A norm which is symmetric enough is induced by an inner product?
- Counting non-isomorphic relations
- product distribution of two uniform distribution, what about 3 or more
- Find the value of $\sqrt{10\sqrt{10\sqrt{10…}}}$
- How can I prove the convergence of a power-tower?
- Is $\sum_{n=1}^\infty {1\over 3^{\sqrt{n}}}$ convergent?
- Chance on winning by throwing a head on first toss.
- How to arrive at Ramanujan nested radical identity
- Does every continuous time minimal Markov chain have the Feller property?