List questions from quotient-spaces

Published on 10 Nov 2015 - 20:34

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Let $f = \prod_{i=1}^n (X - z_i)^{r_i} \in \mathbb{C}[x]$. Prove that $\mathbb{C}[x]/(f) \simeq \prod_{i=1}^n \mathbb{C}[x]/(X-z_i)^{r_i}$

Published on 10 Nov 2015 - 23:00

122

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Find a polynomial $q(x)$ of minimal degree in $F_3[x]$ so that the following condition is true:

Published on 30 Mar 2026 - 8:57

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What does it mean that in a factor/quotient group certain elements get "glued" together

Published on 22 Mar 2026 - 15:18

557

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Why is the quotient map from a Banach space open with respect to the weak topologies?

Published on 26 Mar 2026 - 14:44

116

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Identification Topology (Mendelson's 'Introduction to Topology', page 103)

Published on 25 Nov 2015 - 6:07

123

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Quotient group of invertible matrices isomorphic to $\mathbb{R}\times$

Published on 25 Nov 2015 - 14:30

124

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Some insights in quotient topologies

Published on 25 Nov 2015 - 21:08

1.1k

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Quotient ring by ideal generated by several elements in steps.

Published on 26 Nov 2015 - 19:31

100

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Quotient Space Notation

Published on 30 Nov 2015 - 3:39

115

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Collapsing the Unit Ball in $\mathbb{R}^n$

Published on 01 Dec 2015 - 22:15

253

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Calculating quotient ring over polynomial ring without guessing

Published on 02 Dec 2015 - 18:21

58

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Strange endomorphism that translates in a functor one (?)

Published on 04 Dec 2015 - 17:32

192

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Evaluation of a formal series at a point

Published on 27 Mar 2026 - 6:34

177

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If $X/F$ is separable, must $X/F$ isomorphic to $F$?

Published on 05 Dec 2015 - 6:20

List Question

How to verify the inverse of a polynomial in mod polynomial?

Let $f = \prod_{i=1}^n (X - z_i)^{r_i} \in \mathbb{C}[x]$. Prove that $\mathbb{C}[x]/(f) \simeq \prod_{i=1}^n \mathbb{C}[x]/(X-z_i)^{r_i}$

Find a polynomial $q(x)$ of minimal degree in $F_3[x]$ so that the following condition is true:

What does it mean that in a factor/quotient group certain elements get "glued" together

Why is the quotient map from a Banach space open with respect to the weak topologies?

Identification Topology (Mendelson's 'Introduction to Topology', page 103)

Quotient group of invertible matrices isomorphic to $\mathbb{R}\times$

Some insights in quotient topologies

Quotient ring by ideal generated by several elements in steps.

Quotient Space Notation

Collapsing the Unit Ball in $\mathbb{R}^n$

Calculating quotient ring over polynomial ring without guessing

Strange endomorphism that translates in a functor one (?)

Evaluation of a formal series at a point

If $X/F$ is separable, must $X/F$ isomorphic to $F$?

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