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6 votes

Where does $\pi^2$ appear spontaneously within Physical Phenomenon and Mathematics Equations?

answered Jul 21, 2019 at 12:20

6 votes

Accepted

Does there exist a surjective group homomorphism $\varphi:A_4\rightarrow\mathbb{Z}/4\mathbb{Z}$?

answered May 20, 2022 at 0:04

5 votes

Accepted

If an $R$-module $M \cong M \oplus M$ then if $S=\operatorname{Hom}_R(M,M)$ we have $S \cong S \oplus S$

answered Jul 23, 2019 at 14:45

4 votes

Accepted

Let $R:=\mathbb{Z}[\sqrt{-6}]$. Prove that $R$ is not a Unique Factorization Domain

answered Mar 9, 2022 at 4:23

4 votes

Accepted

Irreducible polynomial in $\mathbb{F}_p[x]$ divides $x^{p^n}-x$

answered Nov 14, 2020 at 18:17

3 votes

Homomorphisms from $\mathbb{Z}[x] \to R$

answered Jan 23, 2021 at 18:37

2 votes

Accepted

Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

answered Nov 15, 2020 at 8:25

2 votes

Why cant $a_n$ be zero in a polynomial function?

answered Jul 13, 2020 at 11:12

2 votes

What is the center of $End_A(S)$?

answered Aug 29, 2020 at 18:04

2 votes

Accepted

Difference between permutation and combination

answered Sep 20, 2020 at 6:30

2 votes

Prove that field $\mathbb{Z}[x]/(x,3)$ is isomorphic to field $\mathbb{Z}/3\mathbb{Z}$.

answered May 25, 2020 at 10:48

2 votes

Accepted

Exact sequence in which $M/\operatorname{Ker}f$ and $\operatorname{Im}f$ appear

answered Jun 22, 2022 at 12:03

2 votes

Can we know the equation of line " $L$ " from one point $P(a,b)$ in this line?

answered Nov 14, 2020 at 17:01

2 votes

Accepted

finding all automorphism of $\mathbb{Q}(\sqrt[4]{2})/\mathbb{Q}(\sqrt{2})$

answered Apr 30, 2021 at 14:48

2 votes

$p^i\mathbb {Z}_p$ is an open subgroup of $\mathbb {Z}_p$ of index $p^i$, where $\mathbb {Z}_p$ is the group of p-adic integers

answered Jul 12, 2019 at 8:27

2 votes

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

answered May 10, 2020 at 7:55

2 votes

Question about Elliptic curves over finite field and Frobenius morphism

answered May 24, 2020 at 11:48

2 votes

How to show $\mathbb Z_2[x]/(x^3+x+1)$ is isomorphic to $\mathbb Z_2[x]/(x^3+x^2+1)$

answered Apr 8, 2019 at 3:42

2 votes

Accepted

finite set with infinite closure (topology)

answered Sep 18, 2015 at 2:06

2 votes

Find $\lim\limits_{n\to \infty}x_{n}$ if for all $n\ge 1$ $\{x_n\}$denotes a sequence of real numbers where $x_{n+1}=\frac{1}{2}(x_n+\frac{5}{x_n})$

answered Apr 26, 2018 at 11:38

2 votes

Examples of homeomorphic topological spaces

answered Jan 31, 2017 at 2:40

2 votes

Prove that there are no convex functions on compact manifolds

answered Feb 7, 2018 at 13:07

2 votes

Accepted

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

answered Dec 30, 2018 at 12:59

1 vote

Is the set $\{ (x,\sin(\frac{1}{x}) ) | x \in (0,1)\}$ a manifold with and without the origin

answered Mar 21, 2019 at 19:05

1 vote

Continous map $X \to \{0,1\} \iff \text {X is disconnected}$

answered Jan 31, 2017 at 21:55

1 vote

Accepted

If $\alpha, \beta, \gamma$ are the roots of the cubic $\ ax^3+bx^2+cx+d$, show that $\alpha\beta+\alpha\gamma+\beta\gamma=\frac{c}{a}$.

answered Nov 24, 2018 at 13:55

1 vote

How do I factor the polynomial $x^3−5x^2+7x+13$ completely?

answered Nov 29, 2018 at 5:24

1 vote

If $A\subset K$ and $K$ compact, does $\bar A$ compact?

answered Aug 29, 2018 at 10:33

1 vote

Inverse of an element of the group $\mathbb{Z}_n$ under addition $\pmod{n}$

answered Sep 12, 2018 at 9:41

1 vote

1st order pde and lagrange method.

answered Dec 31, 2016 at 11:48

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69 Answers

Where does $\pi^2$ appear spontaneously within Physical Phenomenon and Mathematics Equations?

Does there exist a surjective group homomorphism $\varphi:A_4\rightarrow\mathbb{Z}/4\mathbb{Z}$?

If an $R$-module $M \cong M \oplus M$ then if $S=\operatorname{Hom}_R(M,M)$ we have $S \cong S \oplus S$

Let $R:=\mathbb{Z}[\sqrt{-6}]$. Prove that $R$ is not a Unique Factorization Domain

Irreducible polynomial in $\mathbb{F}_p[x]$ divides $x^{p^n}-x$

Homomorphisms from $\mathbb{Z}[x] \to R$

Let $F$ be an infinite field and let $f(x) ∈ F[x]$. If $f(a) = 0$ for infinitely many $a ∈ F$, show that $f = 0$.

Why cant $a_n$ be zero in a polynomial function?

What is the center of $End_A(S)$?

Difference between permutation and combination

Prove that field $\mathbb{Z}[x]/(x,3)$ is isomorphic to field $\mathbb{Z}/3\mathbb{Z}$.

Exact sequence in which $M/\operatorname{Ker}f$ and $\operatorname{Im}f$ appear

Can we know the equation of line " $L$ " from one point $P(a,b)$ in this line?

finding all automorphism of $\mathbb{Q}(\sqrt[4]{2})/\mathbb{Q}(\sqrt{2})$

$p^i\mathbb {Z}_p$ is an open subgroup of $\mathbb {Z}_p$ of index $p^i$, where $\mathbb {Z}_p$ is the group of p-adic integers

Prove$(2,x^2+x+1)$ is a maximal ideal of $\mathbb{Z}[x]$

Question about Elliptic curves over finite field and Frobenius morphism

How to show $\mathbb Z_2[x]/(x^3+x+1)$ is isomorphic to $\mathbb Z_2[x]/(x^3+x^2+1)$

finite set with infinite closure (topology)

Find $\lim\limits_{n\to \infty}x_{n}$ if for all $n\ge 1$ $\{x_n\}$denotes a sequence of real numbers where $x_{n+1}=\frac{1}{2}(x_n+\frac{5}{x_n})$

Examples of homeomorphic topological spaces

Prove that there are no convex functions on compact manifolds

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

Is the set $\{ (x,\sin(\frac{1}{x}) ) | x \in (0,1)\}$ a manifold with and without the origin

Continous map $X \to \{0,1\} \iff \text {X is disconnected}$

If $\alpha, \beta, \gamma$ are the roots of the cubic $\ ax^3+bx^2+cx+d$, show that $\alpha\beta+\alpha\gamma+\beta\gamma=\frac{c}{a}$.

How do I factor the polynomial $x^3−5x^2+7x+13$ completely?

If $A\subset K$ and $K$ compact, does $\bar A$ compact?

Inverse of an element of the group $\mathbb{Z}_n$ under addition $\pmod{n}$

1st order pde and lagrange method.