Hello. I thank for your answer, in advance. Let $G$ be a finite group and $G$ has an element of order $n$ such that $\pi(n)=\pi(G)$ where $\pi(n)$ denote the set of prime divisors …

Let $R$ be a commutative, finitely generated $\mathbb{Z}$-algebra, then the nil radical is equal to the Jacobson radical. I am not able to make much traction on this, nor can I fi …

If you take a subtraction-free rational identity like $(xxx+yyy)/(x+y)+xy=xx+yy$ and replace $\times$,$/$,$+$,$1$ by $+$,$-$,min,$0$, do you always get a valid min,plus,minus ident …

SETUP: Assume $f(\cdot)$ is continuous and strictly monotone decreasing on $[0,\infty]$, with $f(0)>0$ and $f(\infty)<0$. Let $x_m$ be the solution of $\frac{1}{m}\sum_{i=1}^{ …

The p-adic Weiestrass lemma asserts that a power series $f(z)$ with coefficients in the ring of integers of a local field can be factored as $π^n·u(z)·p(z)$ where u(z) is a unit in …

In Van der Waerden B L. Algebra Vol.I[M]. Springer, 2003, Pro. Waerden announced in page 256 that if an element $\gamma$ of a formally real field K is not a sum of squares, there e …

We know that for finding the solutions of PDE equations, one of methods is "reduction of PDE", . For nonlinear equation $v_t=(v^{-4/3}v_x)_x+\lambda v$ how can we compute the gen …

In relation to my question http://mathoverflow.net/questions/123058/expression-for-the-sum-of-square-roots-of-zeros-of-a-polynomial How to characterize polynomials $f(x)$ with rat …

How does the idea of a "minimal polynomial" for a matrix (i.e. for a matrix $A$, the polynomial, $\mu (x)$, of least degree, such that $\mu (A) =0$) relate the the "minimal polynom …

For a given a bivariate polynomial $P(x,y)$ with rational coefficients: Q1. How compute such (invertible) substitutions of its variables that would transform the polynomial into a …

Hello, for my bachelor's thesis I need to understand the Hopf Algebra of Feynman Diagrams. As I have only litte knowledge in Algebra by now I wanted to ask where I could start and …

Background and Motivation I've always been fascinated about algebraic statements independent from ZFC set theory. One such fascinating example comes from considering $\rm{Ext}^1_\ …

It is clear that the permanent of an $n\times n$ matrix which entries are odd integers, is an even number, as it is the sum of $n!$ odd numbers. I am interested in finding the high …

Does there exist a lattice-ordered group of rational rank $1$? This is true for totally ordered group.

I wonder if there is a simple closed form solution to the following sum: $\sum_{k = 1}^n \frac{(1/2)^k}{k}$? Wolfram Alpha expresses it in terms of the Lerch transcendent, but I wo …