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kpax
  • Member for 10 years, 8 months
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23 votes
2 answers
4k views

A problem about an $R$-module that is both injective and projective.

9 votes
1 answer
320 views

A finite unital and commutative ring with exactly one maximal ideal has $p^{n}$ elements.

9 votes
1 answer
2k views

If $G$ is an infinite group, then the group ring $R(G)$ is not semisimple.

8 votes
2 answers
579 views

examples of additive categories which have morphism that has no kernel and morphism has no cokernels.

8 votes
1 answer
2k views

suppose $n$ people are in a party and every two of them have exactly one common friends,prove that there is one who is friend to all.

8 votes
2 answers
367 views

suppose that $n$ is natural number and even, show that $n \nmid 1^n +2^n+3^n + \ldots (n-1)^n$.

7 votes
1 answer
3k views

what is the homology groups some quotient space of torus

6 votes
1 answer
1k views

Let $f$ be a morphism of chain complexes. Show that if $ker(f)$ and $coker(f)$ are acyclic, then $f$ is a quasi-isomorphism.

5 votes
2 answers
2k views

prove or supply counter example about graph

5 votes
2 answers
1k views

$S^2$ with countably many points removed is path-connected

5 votes
1 answer
358 views

Ring epimorphism $f:R\rightarrow S$, $R$ has finitely many maximal ideals, then $f(J(R))=J(S)$.

5 votes
2 answers
942 views

Can we make the real numbers a $\mathbb{C}$-vector space?

5 votes
2 answers
1k views

Show that the union of the spheres of radius $\frac{1}{n}$ and center $(\frac{1}{n},0,0)$ is simply-connected.

5 votes
3 answers
2k views

how should I show that it is wedge of infinite circles?

5 votes
2 answers
149 views

If the function $\varphi \colon Z\rightarrow C(X,Y)$ is continuous then $F\colon Z\times X\rightarrow Y$, $F(z,x)=\varphi (z)(x)$ will be continuous.

5 votes
1 answer
2k views

$\exists c>0$, $\forall A\subseteq \Bbb R_{\ne 0}$ s.t. $|A|=n$, $\exists B\subseteq A$ s.t. $|B|>cn$ & $b_1+2b_2=2b_3+2b_3$ has no solutions in $B$.

5 votes
0 answers
2k views

what is the covering space of figure eight which is corresponding to commutator subgroup.

5 votes
1 answer
178 views

Why $|G:Z(G)|$ is finite in this question?

4 votes
2 answers
103 views

Prove that a graph which is constructed with matrices is strongly regular

4 votes
1 answer
348 views

Prove that $h< \frac{(k+l)^{k+l}}{(k^{k}l^{l})}$.

4 votes
1 answer
199 views

Prove that $M_{n}(F)\otimes _{F}M_{m}(F)\simeq M_{nm}(F)$ .

4 votes
1 answer
2k views

An example of ideal that has no primary decomposition.

4 votes
2 answers
859 views

A finite ring whose the only nilpotent element is zero is isomorphic to a direct product of fields.

4 votes
1 answer
252 views

If $f\in\hbox{Hom}_{\mathbb{Z}}(\prod_{i=1}^{\infty }\mathbb{Z},\mathbb{Z})$ and $f\mid_{\bigoplus_{i=1}^{\infty } \mathbb{Z}}=0$ then $f=0$.

3 votes
1 answer
384 views

exercise 6.15 from joseph rotman's introduction to homological algebra .

3 votes
1 answer
86 views

prove that $D_8 \cong C_2 \wr C_2$ .

3 votes
1 answer
375 views

Prove that $J$ is an injective module.

3 votes
1 answer
672 views

Prove that if $P$ and $Q$ are projective and finitely generated $R$-modules then $\operatorname{Hom}_{R}(P,Q)$ is projective and finitely generated.

3 votes
1 answer
503 views

If $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ is exact and $B\simeq A\oplus C$ as a $R$-module, does this sequence split? [duplicate]

3 votes
0 answers
340 views

showing that $\Phi:\Pi_{1}(X,x_{0})\rightarrow [S^{1},X]$ is onto if $X$ is path connected. [duplicate]

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