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Proposition 4.7 on Lang's semisimple rings part.

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#abstract-algebra #ring-theory #modules #semi-simple-rings
86
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Identifying $\mathbb{C} D_8$ as a product of matrix rings

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#abstract-algebra #group-theory #ring-theory #representation-theory #semi-simple-rings
464
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If $k$ is a field of characteristic $p>0$ and $G$ is a finite group of order divisible by $p$ then $k[G]$ is not a semi-simple ring.

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#abstract-algebra #ring-theory #noncommutative-algebra #group-rings #semi-simple-rings
834
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primitive idempotents in semisimple rings

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#idempotents #semi-simple-rings
2.2k
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What are the possible $2\times 2$ semisimple matrices?

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#linear-algebra #matrices #semi-simple-rings
50
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Isn't any algebra with finite composition length and non-isomorphic simple modules semisimple?

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#abstract-algebra #modules #representation-theory #semi-simple-rings
48
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Product of semisimple rings is semisimple.

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#abstract-algebra #semi-simple-rings
32
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Subalgebra with semisimple centralizer itself semisimple?

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#abstract-algebra #modules #representation-theory #noncommutative-algebra #semi-simple-rings
62
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Isomorphism of matrix ring with elements from opposite ring

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#linear-algebra #abstract-algebra #matrices #ring-theory #semi-simple-rings
30
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Cocenter is a free module over the center in a semisimple ring

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#abstract-algebra #ring-theory #semi-simple-rings
59
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stably free modules over semisimple rings are free

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#solution-verification #semi-simple-rings
41
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stable range of stably free modules

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#solution-verification #projective-module #artinian #algebraic-k-theory #semi-simple-rings
50
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One sided ideals of a semisimple ring.

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#abstract-algebra #ring-theory #ideals #direct-product #semi-simple-rings
80
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A PID is a semisimple ring iff it is a field

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#abstract-algebra #solution-verification #representation-theory #principal-ideal-domains #semi-simple-rings
38
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Primitive idempotent in semisimple ring

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#abstract-algebra #ring-theory #semi-simple-rings

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