User Rabi Kumar Chakraborty

14 votes

2 answers

541 views

On a ring $R$ such that every subring of $R$ is an ideal .

asked Sep 30, 2019 at 17:53

7 votes

2 answers

142 views

A problem regarding the rank of a matrix

linear-algebra matrices matrix-rank

asked Jan 19, 2020 at 14:51

5 votes

4 answers

117 views

A problem regarding the in-equality of complex numbers .

complex-analysis complex-numbers triangle-inequality

asked Mar 4, 2020 at 6:28

5 votes

0 answers

210 views

A problem on group homomorphism .

abstract-algebra group-homomorphism

asked Jul 27, 2019 at 16:06

5 votes

1 answer

68 views

On isomorphism of two quotient of polynomial rings

abstract-algebra ring-theory irreducible-polynomials unique-factorization-domains

asked Feb 3, 2021 at 16:33

4 votes

0 answers

97 views

Is $\sqrt {f(x)}$ infinitely differentiable? [duplicate]

real-analysis

asked Aug 3, 2019 at 3:01

4 votes

1 answer

65 views

A problem regarding the conjugacy classes of homeomorphism group .

general-topology functional-equations

asked Mar 10, 2020 at 18:08

3 votes

2 answers

135 views

Does $-1$ have a square root in the ring $\frac{\mathbb R[x]}{\langle(x^2+1)^2\rangle}$? [duplicate]

abstract-algebra ring-theory irreducible-polynomials

asked Mar 2, 2020 at 9:28

3 votes

1 answer

82 views

A problem regarding the product of all the elements of $U_n$ for some selected $n$

abstract-algebra abelian-groups multiplicative-function

asked Apr 8, 2020 at 10:20

3 votes

4 answers

147 views

Evaluate the following limit: $\lim_{k \to \infty} \int_0^1 e^{- (k^2x^2/2)} dx$

real-analysis limits

asked Aug 9, 2019 at 20:02

3 votes

2 answers

111 views

Problem on the compactness of a subset of $\mathsf{M}_n(\mathbb{R})$

general-topology compactness

asked Jul 24, 2019 at 3:32

3 votes

1 answer

283 views

If in a group $G$ , $(ab)^2=(ba)^2$ for all $a,b \in G$ , then show that $G$ is abelian .

group-theory

asked Jul 22, 2018 at 17:20

3 votes

2 answers

431 views

Show that the function $f(x)= \arcsin(x)$ is Lipschitz on $[-1,1]$

real-analysis

asked Jul 26, 2018 at 17:38

3 votes

1 answer

165 views

Is there any underlying relationship between an even function and a symmetric matrix , as well as an odd function and a skew symmetric matrix?

linear-algebra

asked Sep 6, 2018 at 4:24

3 votes

1 answer

67 views

In a metric space $X$, the boundary of an open set is the set of all limit points of a discrete set .

general-topology metric-spaces axiom-of-choice

asked Jun 22, 2019 at 8:34

3 votes

1 answer

484 views

If A is an $n\times n$ square matrix such that $A^3=A$ , then show that $\operatorname{rank}(A) + \operatorname{tr}(A)$ is even

linear-algebra matrix-rank

asked Jul 13, 2019 at 2:44

3 votes

0 answers

100 views

Linear isometry between $\mathcal l_p$ and $\mathcal l_q$ norms in $\mathbb R^n$ implies $p$ and $q$ are conjugate exponents

real-analysis linear-algebra functional-analysis normed-spaces isometry

asked Mar 19, 2021 at 17:28

3 votes

3 answers

254 views

$X=H - \{(0,0)\}$ is contractible where $H =\{(x,y) | y\geq 0\}$

general-topology algebraic-topology homotopy-theory

asked Sep 22, 2021 at 18:04

2 votes

1 answer

51 views

Problem on finding integral submanifold of a smooth rank-$2$ distribution .

differential-geometry vector-fields submanifold

asked Nov 28, 2021 at 10:53

2 votes

2 answers

135 views

The quotient field of an unique factorisation domain is never algebraically closed .

abstract-algebra ring-theory field-theory galois-theory unique-factorization-domains

asked May 7, 2021 at 16:34

2 votes

0 answers

68 views

Show that if $n$ is odd, then $\frac {RP^n}{RP^{n-2}} \simeq S^n \vee S^{n-1} $

general-topology algebraic-topology quotient-spaces projective-space

asked Jul 22, 2021 at 21:05

2 votes

1 answer

65 views

Computing limits in matrix exponential

linear-algebra functional-analysis banach-spaces normed-spaces matrix-exponential

asked Dec 14, 2020 at 15:49

2 votes

1 answer

70 views

Is Banach algebra $L^1(\mathbb T)$ under convolution a division algebra?

real-analysis fourier-analysis convolution banach-algebras

asked Jan 11 at 11:51

2 votes

0 answers

35 views

On convergence of the same sequence under two different norms.

real-analysis functional-analysis fourier-analysis lp-spaces

asked Jan 24 at 14:34

2 votes

1 answer

44 views

A question on group representation .

abstract-algebra finite-groups

asked Jun 27, 2019 at 3:14

2 votes

3 answers

135 views

Cardinality of the family of all possible connected subsets of $\Bbb R^n$

general-topology connectedness

asked Jun 16, 2019 at 19:09

2 votes

0 answers

81 views

Test either the following series is convergent or not : $(\cos{1})+(\cos{2})^2+(\cos{3})^3+(\cos{4})^4+...+(\cos{n})^n+...$

real-analysis sequences-and-series analysis

asked Nov 3, 2018 at 8:35

2 votes

0 answers

55 views

A problem regarding polynomials with only prime powers [duplicate]

abstract-algebra ring-theory irreducible-polynomials principal-ideal-domains

asked Jun 2, 2020 at 20:42

2 votes

2 answers

72 views

A problem regarding the ratios $\frac{f(x)}{g(x)}$ and $\frac{g(x)}{h(x)}$, assuming $f(x)g(y) = h\big(\sqrt{x^2+y^2}\big)$

analysis functions functional-equations

asked Jun 4, 2020 at 15:00

2 votes

2 answers

35 views

A problem regarding the value of the derivative of a real valued function

real-analysis functions derivatives

asked Jun 10, 2020 at 12:24

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121 Questions

On a ring $R$ such that every subring of $R$ is an ideal .

A problem regarding the rank of a matrix

A problem regarding the in-equality of complex numbers .

A problem on group homomorphism .

On isomorphism of two quotient of polynomial rings

Is $\sqrt {f(x)}$ infinitely differentiable? [duplicate]

A problem regarding the conjugacy classes of homeomorphism group .

Does $-1$ have a square root in the ring $\frac{\mathbb R[x]}{\langle(x^2+1)^2\rangle}$? [duplicate]

A problem regarding the product of all the elements of $U_n$ for some selected $n$

Evaluate the following limit: $\lim_{k \to \infty} \int_0^1 e^{- (k^2x^2/2)} dx$

Problem on the compactness of a subset of $\mathsf{M}_n(\mathbb{R})$

If in a group $G$ , $(ab)^2=(ba)^2$ for all $a,b \in G$ , then show that $G$ is abelian .

Show that the function $f(x)= \arcsin(x)$ is Lipschitz on $[-1,1]$

Is there any underlying relationship between an even function and a symmetric matrix , as well as an odd function and a skew symmetric matrix?

In a metric space $X$, the boundary of an open set is the set of all limit points of a discrete set .

If A is an $n\times n$ square matrix such that $A^3=A$ , then show that $\operatorname{rank}(A) + \operatorname{tr}(A)$ is even

Linear isometry between $\mathcal l_p$ and $\mathcal l_q$ norms in $\mathbb R^n$ implies $p$ and $q$ are conjugate exponents

$X=H - \{(0,0)\}$ is contractible where $H =\{(x,y) | y\geq 0\}$

Problem on finding integral submanifold of a smooth rank-$2$ distribution .

The quotient field of an unique factorisation domain is never algebraically closed .

Show that if $n$ is odd, then $\frac {RP^n}{RP^{n-2}} \simeq S^n \vee S^{n-1} $

Computing limits in matrix exponential

Is Banach algebra $L^1(\mathbb T)$ under convolution a division algebra?

On convergence of the same sequence under two different norms.

A question on group representation .

Cardinality of the family of all possible connected subsets of $\Bbb R^n$

Test either the following series is convergent or not : $(\cos{1})+(\cos{2})^2+(\cos{3})^3+(\cos{4})^4+...+(\cos{n})^n+...$

A problem regarding polynomials with only prime powers [duplicate]

A problem regarding the ratios $\frac{f(x)}{g(x)}$ and $\frac{g(x)}{h(x)}$, assuming $f(x)g(y) = h\big(\sqrt{x^2+y^2}\big)$

A problem regarding the value of the derivative of a real valued function