Martin Brandenburg

Berlin, Germany

You can contact me via email if you have questions or comments about my research. Please understand that I don't respond to emails with general questions, and that it is a better idea to post them directly in the forum.

Email: my last name [at] uni [dash] muenster [dot] de
Category theory textbook (German)
List of publications

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A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?

ring-theory commutative-algebra noetherian krull-dimension dimension-theory-algebra asked Apr 11, 2013 at 15:19

math.stackexchange.com

109 votes

Ring structure on the Galois group of a finite field

abstract-algebra ring-theory field-theory galois-theory finite-fields asked Nov 17, 2013 at 7:19

math.stackexchange.com

103 votes

A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?

ac.commutative-algebra krull-dimension asked Jun 21, 2014 at 8:10

mathoverflow.net

91 votes

$A$ is isomorphic to $A \oplus \mathbb{Z}^2$, but not to $A \oplus \mathbb{Z}$

gr.group-theory ra.rings-and-algebras examples abelian-groups asked Sep 12, 2015 at 8:20

mathoverflow.net

87 votes

When is $A$ isomorphic to $A^3$?

gr.group-theory ra.rings-and-algebras asked Dec 30, 2009 at 11:56

mathoverflow.net

76 votes

Rigidity of the category of schemes

ag.algebraic-geometry ct.category-theory asked Feb 28, 2011 at 11:23

mathoverflow.net

74 votes

$R$ is isomorphic to $R[X,Y]$, but not to $R[X]$

ag.algebraic-geometry ac.commutative-algebra ra.rings-and-algebras examples nonnoetherian asked Dec 11, 2015 at 20:53

mathoverflow.net

70 votes

Geometric intuition for the tensor product of vector spaces

linear-algebra geometry intuition tensor-products vector-bundles asked Sep 6, 2013 at 20:02

math.stackexchange.com

66 votes

explicit big linearly independent sets

linear-algebra asked May 1, 2010 at 21:20

mathoverflow.net

65 votes

Results from abstract algebra which look wrong (but are true)

gr.group-theory ra.rings-and-algebras big-list abelian-groups asked Jan 19 at 23:25

mathoverflow.net

Top Answers

290

Examples of common false beliefs in mathematics

mathoverflow.net

174

Nice examples of groups which are not obviously groups

math.stackexchange.com

149

If $AB = I$ then $BA = I$

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Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.

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What are the reasons for considering rings without identity?

mathoverflow.net

Example of an unnatural isomorphism

mathoverflow.net

A non-noetherian ring with noetherian spectrum

math.stackexchange.com

Submodule of free module over a p.i.d. is free even when the module is not finitely generated?

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Counterexamples in algebra?

mathoverflow.net

Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.

math.stackexchange.com

Why is the commutator defined differently for groups and rings?

math.stackexchange.com

What are the monomorphisms in the category of schemes?

mathoverflow.net

Why does the set of all singleton sets not exist?

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Is $A \times B$ the same as $A \oplus B$?

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In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?

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Rings in which every non-unit is a zero divisor

mathoverflow.net

The Rabinowitz Trick

mathoverflow.net

On limits, schemes and Spec functor

math.stackexchange.com

Using the cocycle condition to glue sheaves

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What does the Lefschetz principle (in algebraic geometry) mean exactly?

mathoverflow.net

Is it possible to make integers a field?

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Show that $\sqrt[3]{2+\frac {10} 9\sqrt 3}+\sqrt[3]{2-\frac {10} 9\sqrt 3}=2$

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Definition of a finitely generated $k$ - algebra

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Reference request for translating from Top to C*-alg

mathoverflow.net

Ring-theoretic characterization of open affines?

mathoverflow.net

Are semi-direct products categorical (co)limits?

mathoverflow.net

What is the kernel of the tensor product of two maps?

math.stackexchange.com

Ring of order $p^2$ is commutative.

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The nil-radical is an intersection of all prime ideals proof

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Algebra: Best mental images

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