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Let $A$ be a commutative noetherian ring, $Isubseteq A$ an ideal, $M_alpha$ be $A$-modules, $forallalphain J$. It is easily seen that the $I$-torsion commutes...
Asked on 11/21/2021 by Ivon
2 answerI think I finally managed to prove this exercise from Kelley's general topology on page 77.I would appreciate feedback on it.Let $X$ be the set of all pairs...
Asked on 11/21/2021
1 answerI am having problems with a combinatorial argument and I need some help. I do not do combinatorics so I am not sure what is the best notation for this...
Asked on 11/21/2021 by Sharik
2 answerGiven the polynomials P1 $(x)$ = $2 + x - x^2 - 2x^3$ P2 $(x)$ = $1 + x + 2x^2 + x^3$ P3 $(x)$...
Asked on 11/20/2021 by DuncanK3
1 answerIn Spivak's Diff Geom (vol.1), p.19, he says a closed manifold is non-bounded and compact (A point in boundary has a neighborhood homeomorphic to half-space). I don't know a non-trivial...
Asked on 11/20/2021
3 answerI am trying to solve $$ x^3dx+(y+2)^2dy=0 quad( 1)$$Dividing by $dx$, we can reduce the ODE to seperate variable form, i.e $$ (1) to (y+2)^2y'=-x^3 $$...
Asked on 11/20/2021
4 answerFrom Carothers, Chapter 1, Exercise 34:Suppose that $a_n geq 0$ and $sum_{n=1}^infty a_n< infty$. Give an example showing that $limsup_{nto infty} n a_n > 0$ is possible.Looking...
Asked on 11/20/2021 by akm
1 answerWhile trying to solve a certain integral I was left with these rather silly integral. $$int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} , dx$$$$int_0^{frac{pi}{2}} e^{-a(sin(x)+cos(x))} sin(cos(x)) , dx$$ Any headway on these...
Asked on 11/20/2021
0 answerLet $omega$ be primitive $n$-th root of unity. Can we determine all tuples of integers $(c_1, c_2,ldots,c_n) $ such that $$c_1+c_2 omega + c_3 omega^2+cdots+ c_n...
Asked on 11/20/2021
1 answerLet $X_1,X_2,cdots,X_m$ be all nonnegative integer solutions of the equation $x_1+x_2+cdots+x_n=d (n,d in mathbb{N^*})$. For example,if $n=2,d=2$,then $m=3$ and $X_1,X_2,X_3=(0,2),(1,1),(2,0)$ or in any other order....
Asked on 11/20/2021 by lsr314
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