User Boris Novikov

45 votes

Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.

answered Mar 19, 2013 at 11:57

43 votes

Why is $\frac{987654321}{123456789} = 8.0000000729?!$

answered May 19, 2013 at 7:46

24 votes

Accepted

if $ab=cd$ then $a+b+c+d $ is composite

answered May 6, 2013 at 15:52

15 votes

Accepted

Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions

answered Mar 30, 2013 at 16:27

15 votes

Good math bed-time stories for children?

answered Nov 7, 2013 at 21:32

14 votes

Accepted

Concept of a subring in Atiyah-Macdonald's book

answered Sep 24, 2013 at 14:58

13 votes

Torsion Subgroup (Just a set) for an abelian (non abelian) group.

answered Aug 16, 2013 at 11:31

13 votes

$G$ is Abelian if it has no element of order $2$ and $(ab)^2=(ba)^2$

answered Nov 14, 2013 at 16:44

11 votes

Accepted

Do Boolean rings always have a unit element?

answered May 14, 2013 at 8:44

10 votes

Groups of order 2k have a normal subgroup of order k and odd permutations

answered Jul 6, 2013 at 8:46

9 votes

Accepted

Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.

answered Aug 12, 2013 at 12:33

9 votes

Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.

answered May 24, 2013 at 22:00

9 votes

Accepted

Atiyah-Macdonald, Proposition 2.12, uniqueness of the tensor product.

answered Jun 15, 2013 at 12:51

9 votes

Ring theory reference books

answered Mar 24, 2013 at 10:45

9 votes

Accepted

$\lim_{n\to\infty}(\sqrt{n^2+n}-\sqrt{n^2+1})$

answered Mar 10, 2013 at 8:35

9 votes

If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?

answered Oct 29, 2013 at 10:29

9 votes

solve trigonometric equation $\cos(2x) + \cos\left(x\right) -2 = 0$

answered Dec 2, 2013 at 18:45

8 votes

Show that $\gcd(a,b)=\operatorname{lcm}(a,b)$ if and only if $a=b$.

answered Sep 23, 2013 at 16:30

8 votes

How can I find the value of $\ln( |x|)$ without using the calculator?

answered Oct 18, 2013 at 12:48

8 votes

Status of the classification of non-finitely generated abelian groups.

answered Feb 25, 2013 at 8:18

8 votes

How do I sell out with abstract algebra?

answered Apr 21, 2013 at 7:09

8 votes

How did we know to invent homological algebra?

answered Jun 10, 2013 at 20:03

8 votes

Accepted

Where can I learn about the lattice of partitions?

answered Jun 1, 2013 at 15:45

8 votes

Accepted

What is the mathematical foundation of Control Theory?

answered May 19, 2013 at 15:34

8 votes

Accepted

Find $S$ where $S=\sqrt[3] {5+2 \sqrt {13}}+\sqrt[3]{5-2 \sqrt {13}}$, why am I getting an imaginary number?

answered Jun 28, 2013 at 14:29

7 votes

Accepted

Structure theorem for finitely generated commutative $semi$groups.

answered Jun 29, 2013 at 16:39

7 votes

If $G$ is a finite group, $H$ is a subgroup of $G$, and there is an element of $G/H$ of order $n$, then there is an element of $G$ of order $n$

answered Aug 11, 2013 at 8:18

7 votes

What can we say about the size of $HK\cap KH$ when $HK\neq KH$?

answered May 11, 2013 at 9:36

7 votes

Can we embed cancellative rings into division rings?

answered Mar 21, 2013 at 14:26

7 votes

Can the square of a proper ideal be equal to the ideal?

answered Apr 2, 2013 at 6:45

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546 Answers

Prove that the additive group $ℚ$ is not isomorphic with the multiplicative group $ℚ^*$.

Why is $\frac{987654321}{123456789} = 8.0000000729?!$

if $ab=cd$ then $a+b+c+d $ is composite

Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions

Good math bed-time stories for children?

Concept of a subring in Atiyah-Macdonald's book

Torsion Subgroup (Just a set) for an abelian (non abelian) group.

$G$ is Abelian if it has no element of order $2$ and $(ab)^2=(ba)^2$

Do Boolean rings always have a unit element?

Groups of order 2k have a normal subgroup of order k and odd permutations

Let $G$ be abelian, $H$ and $K$ subgroups of orders $n$, $m$. Then G has subgroup of order $\operatorname{lcm}(n,m)$.

Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.

Atiyah-Macdonald, Proposition 2.12, uniqueness of the tensor product.

Ring theory reference books

$\lim_{n\to\infty}(\sqrt{n^2+n}-\sqrt{n^2+1})$

If $H_1, H_2\leq G$ are such that $H_1\cong H_2$ then $G/H_1\cong G/H_2$?

solve trigonometric equation $\cos(2x) + \cos\left(x\right) -2 = 0$

Show that $\gcd(a,b)=\operatorname{lcm}(a,b)$ if and only if $a=b$.

How can I find the value of $\ln( |x|)$ without using the calculator?

Status of the classification of non-finitely generated abelian groups.

How do I sell out with abstract algebra?

How did we know to invent homological algebra?

Where can I learn about the lattice of partitions?

What is the mathematical foundation of Control Theory?

Find $S$ where $S=\sqrt[3] {5+2 \sqrt {13}}+\sqrt[3]{5-2 \sqrt {13}}$, why am I getting an imaginary number?

Structure theorem for finitely generated commutative $semi$groups.

If $G$ is a finite group, $H$ is a subgroup of $G$, and there is an element of $G/H$ of order $n$, then there is an element of $G$ of order $n$

What can we say about the size of $HK\cap KH$ when $HK\neq KH$?

Can we embed cancellative rings into division rings?

Can the square of a proper ideal be equal to the ideal?