Some problems in Noncommutative Algebra book of Benson Farb and R. Keith Dennis
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Show for any simple ring without identity, R, that R is a division ring.
26764
Proving that $\mathbb R^3$ cannot be made into a real division algebra (and that extending complex multiplication would not work)
54198
algebra - matrices and polynoms
24561
$\mathbb S_n$ as semidirect product
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Probs. 12 & 13 , Sec. 2.3, in Herstein's TOPICS IN ALGEBRA, 2nd ed: Existence of only right-sided identity and right-sided inverses suffice
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Prove that $\mathfrak{su}(2)$ is not isomorphic to $\mathfrak{sl}(2,\mathbb R)$
72295
A difficulty in understanding the proof of distributivity of tensor products over direct sums for modules.
137029
Prove that $\operatorname{Hom}_{\Bbb{Z}}(\Bbb{Q},\Bbb{Z}) = 0$ and show that $\Bbb{Q}$ is not a projective $\Bbb{Z}$-module.
151251
A simple algebra that is not semisimple
78873
How to show that the monomials are not a Schauder basis for $C[0,1]$
144211
a second course in abstract algebra
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strictly positive elements in $C^*$-algebra
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Problem from Herstein on group theory
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Showing $[(fg)h]_n = [f(gh)_n]$ in the linear algebra $F^\infty$
109688
Zero-dimensional ideals and finite-dimensional algebras
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On the nilpotence of the matrix $AB-BA$
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The characteristic and minimal polynomial of a companion matrix