Intereting Posts

Give an example of a relation R on $A^2$ which is reflexive, symmetric, and not transitive
“Number of Decompositions into $k$ Powers of $p$”-Counting Functions
Question about weak convergence, $\lbrace f(x_{n}) \rbrace$ converges for all $n$, then $x_{n} \rightharpoonup x$
Sum identity using Stirling numbers of the second kind
Are the integers closed under addition… really?
Is there another way to solve this integral?
What can we say about $f$ if $\int_0^1 f(x)p(x)dx=0$ for all polynomials $p$?
Calculating Bernoulli Numbers from $\sum_{n=0}^\infty\frac{B_nx^n}{n!}=\frac x{e^x-1}$
Extended Pythagorean Theorem
Non-finitely generated, non-projective flat module, over a polynomial ring
Prove or Disprove: If every nontrivial subgroup of a group $G$ is cyclic, then $G$ is cyclic.
Poincare dual of unit circle
Intuition for the Product of Vector and Matrices: $x^TAx $
Proving Gauss' polynomial theorem (Rational Root Test)
Is $dx\,dy$ really a multiplication of $dx$ and $dy$?

Let $R$ be a commutative noetherian ring, and let $M$ be an $R$-module. How can I show that if any localization $M_p$ at a prime ideal $p$ of the ring $R$ is injective over $R_p$, then $M$ is injective?

- $\mathbb{Q}/(X^2+Y^2-1)$ is integrally closed
- Hensel lift of a monic polynomial over $F_{2}$ in $Z_{8}$
- What are some examples of principal, proper ideals that have height at least $2$?
- Show that $k/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
- Is an ideal generated by multilinear polynomials of different degrees always radical?
- An example of prime ideal $P$ in an integral domain such that $\bigcap_{n=1}^{\infty}P^n$ is not prime
- Every finitely generated algebra over a field is a Jacobson ring
- Necessary and sufficient condition that a localization of an integral domain is integrally closed
- Ideal defining the nilpotent cone of $\mathfrak{gl}_n(k)$
- If $A$ is reduced, Spec $A$ has no embedded points

Baer’s criterion shows that it suffices to show that $\hom(B,M) \to \hom(A,M)$ is surjective for $B=R$ and $A=$ an ideal, in particular both are finitely presented. But then $\hom$ commutes with localization and we are done.

- Catalan numbers – number of ways to stack coins
- Why does the diophantine equation $x^2+x+1=7^y$ have no integer solutions?
- Approximating Euclidean geometry, restricted to $\mathbb{Q}$
- Decomposition of a degenerate conic
- Classification Theorem for Non-Compact 2-Manifolds? 2-Manifolds With Boundary?
- If $xy$ is a unit, are $x$ and $y$ units?
- Conventions for function notation
- Does this “extension property” for polynomial rings satisfy a universal property?
- What is the set of all functions from $\{0, 1\}$ to $\mathbb{N}$ equinumerous to?
- If $E(X\mid Y)=Z$, $E(Y\mid Z)=X$ and $E(Z\mid X)=Y$, then $X=Y=Z$ almost surely
- Why degree of a reducible projective variety is the sum of the degree of its irreducible components
- Arzela-Ascoli and compactness in $C(X), l^p, L^p$
- Present a function with specific feature
- How to solve $x^3\equiv 10 \pmod{990}$?
- A double inequality with binomials