List questions from examples-counterexamples

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abstract algebra example book

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Are there many compact, zero-dimensional, first-countable spaces with $d(Z)=\mathfrak{c}$?

Published on 12 Apr 2026 - 8:43

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Example of a ring $R$ and ideals $A$ and $B$ of $R$ such that $AB\neq A\cap B$.

Published on 19 Sep 2013 - 15:56

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How to prove if something is false or true?

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Counterexample for the logical argument

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Example of a function that has the Luzin $n$-property and is not absolutely continuous.

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Is there a counter example?

Published on 10 Apr 2026 - 1:26

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A $T_1$ space which is not Hausdorff

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Are there motivating examples for graphs with negative edge weights?

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Can an object be universal with respect to several properties?

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Example of Converge in measure, but not converge point-wise a.e.?

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Example of a group in which the equation $x^2=e$ has more than two solutions

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Can we find a subset of $Spec(R)$ not quasi-compact?

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Example of rings of the same positive characteristic that do not embed into their tensor product?

Published on 13 Apr 2026 - 23:07

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How can I calculate $\mathrm{Spec}(\mathbb{Z}_{(3)})$? And $\mathrm{Spec}(\mathbb{Z}_3)$?

abstract algebra example book

Are there many compact, zero-dimensional, first-countable spaces with $d(Z)=\mathfrak{c}$?

Example of a ring $R$ and ideals $A$ and $B$ of $R$ such that $AB\neq A\cap B$.

How to prove if something is false or true?

Counterexample for the logical argument

Example of a function that has the Luzin $n$-property and is not absolutely continuous.

Is there a counter example?

A $T_1$ space which is not Hausdorff

Are there motivating examples for graphs with negative edge weights?

Can an object be universal with respect to several properties?

Example of Converge in measure, but not converge point-wise a.e.?

Example of a group in which the equation $x^2=e$ has more than two solutions

Can we find a subset of $Spec(R)$ not quasi-compact?

Example of rings of the same positive characteristic that do not embed into their tensor product?

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