Intereting Posts

Is there a continuous positive function whose integral over $(0,\infty)$ converges but whose limit is not zero?
Geometric visualization of covector?
Can the “inducing” vector norm be deduced or “recovered” from an induced norm?
Convexity of the product of two functions in higher dimensions
Integer lattice points on a sphere
Why is the shortest distance between two circles along the segment connecting their centers?
Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
Stokes' theorem: Induced orientation on the boundary of a manifold
How to evaluate limiting value of sums of a specific type
Can the cubic be solved this way?
A conjectured result for $\sum_{n=1}^\infty\frac{(-1)^n\,H_{n/5}}n$
University-level books focusing on intuition?
How to prove $\lim_{n \to \infty} \sqrt{n}(\sqrt{n} – 1) = 0$?
Ideal generated by 3 and $1+\sqrt{-5}$ is not a principal ideal in the ring $\Bbb Z$
What is the difference between Hom and Sheaf Hom?

Given an integral domain $R$, and a left torsion $R$-module $A$ (i.e. $\forall{a}\in A,\exists{r}\in R$ such that $ra=0$) how would you show that $\mathrm{Tor}_n^R(A,B)$ is also a torsion $R$-module?

- How can we show that an abelian group of order <1024 has a set of generators of cardinality <10
- Embedding of free $R$-algebras
- An infinite $p$-group may not be nilpotent
- Homological categories in functional analysis
- Using Nakayama's Lemma to prove isomorphism theorem for finitely generated free modules
- Determining Coefficients of a Finite Degree Polynomial $f$ from the Sequence $\{f(k)\}_{k \in \mathbb{N}}$
- Are two subgroups of a finite $p$-group $G$, of the same order, isomorphic?
- Proof that group is commutative if every element is its inverse (feedback wanted)
- Is the localization of a PID a PID?
- What is the relationship between the second isomorphism theorem and the third one in group theory?

Choose a projective resolution $P_\bullet \to B \to 0$. Then $\mathrm{Tor}_n(A,B) \stackrel{\mathrm{def}}{=} H_n(A \otimes P_\bullet)$. This is a quotient of a submodule of $A \otimes P_n$, so that it suffices to observe that $A \otimes P_n$ is torsion, which is obvious (if $ra=0$ then $r(a \otimes p)=0$).

- Limit of sums of iid random variables which are not square-integrable
- Binomial Coefficients with fractions
- Mean Value Property of Harmonic Function on a Square
- Invertibility of a Kronecker Product
- Is $\mathbb{R}$ an algebraic extension of some proper subfield?
- Programs for precocious prodigies
- Proving that $\int_0^\infty\frac{J_{2a}(2x)~J_{2b}(2x)}{x^{2n+1}}~dx~=~\frac12\cdot\frac{(a+b-n-1)!~(2n)!}{(n+a+b)!~(n+a-b)!~(n-a+b)!}$
- A uniformly continuous function between totally bounded uniform spaces
- Prove the following series $\sum\limits_{s=0}^\infty \frac{1}{(sn)!}$
- Pythagorean triples with additional parameters
- Compactness of set of projections
- Example of neither open nor closed set
- Is it impossible to recover multiplication from the division lattice categorically?
- How to prove the eigenvalues of tridiagonal matrix?
- In what situations is the integral equal to infinity?