List questions from semi-simple-rings

Published on 15 Dec 2015 - 3:08

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If $A$ is a semisimple algebra, then every irreducible $A$-module is cyclic over $A$

Published on 22 Feb 2016 - 11:18

441

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If every cyclic $R$-module is projective, then $R$ is semisimple.

Published on 04 May 2016 - 5:10

257

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Relationship between idempotents in semisimple ring.

Published on 07 May 2016 - 23:57

55

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Simple $\mathbb{C}G$ ring

Published on 20 Apr 2017 - 15:25

596

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Wedderburn components of group algebra over $\mathbb R$

Published on 22 Apr 2017 - 10:33

1.6k

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The exact relationship between Clifford algebras and certain special isomorphic k-algebras

Published on 25 Apr 2017 - 19:30

265

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$\mathbb{Z}/n\mathbb{Z}$ is a semisimple ring provided n is square-free

Published on 19 May 2017 - 6:58

121

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(Ex 3.9 b, Lam) If $R$ is semisimple ring with $aR = I$ a two-side ideal, then prove that $Ra = I$.

Published on 25 May 2017 - 18:01

74

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(Ex 3.13 Lam) Suppose R is a simple, infinite dimensional algebra over a field k. If V is left R module, then V as vsp over k is infinite dimensional.

Published on 26 May 2017 - 20:57

61

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Is $\mathrm{End}_{KS_r}(V)$ semisimple?

Published on 17 Jun 2017 - 17:38

235

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$(eR)_R$ is a semisimple right $R$-module $\implies$ $eRe$ is a semisimple ring

Published on 18 Jun 2017 - 14:14

1.2k

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Is every finite dimensional semisimple algebra over $k$ isomorphic to a direct sum of finitely many matrix algebras over $k$?

Published on 19 Jun 2017 - 15:20

495

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$R_R$ is semisimple $\implies$ $M_R$ is semisimple

Published on 21 Jun 2017 - 21:35

180

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End$_A(A)\cong A$

Published on 27 Jun 2017 - 17:08

List Question

Quotient of semi-simple rings

If $A$ is a semisimple algebra, then every irreducible $A$-module is cyclic over $A$

If every cyclic $R$-module is projective, then $R$ is semisimple.

Relationship between idempotents in semisimple ring.

Simple $\mathbb{C}G$ ring

Wedderburn components of group algebra over $\mathbb R$

The exact relationship between Clifford algebras and certain special isomorphic k-algebras

$\mathbb{Z}/n\mathbb{Z}$ is a semisimple ring provided n is square-free

(Ex 3.9 b, Lam) If $R$ is semisimple ring with $aR = I$ a two-side ideal, then prove that $Ra = I$.

(Ex 3.13 Lam) Suppose R is a simple, infinite dimensional algebra over a field k. If V is left R module, then V as vsp over k is infinite dimensional.

Is $\mathrm{End}_{KS_r}(V)$ semisimple?

$(eR)_R$ is a semisimple right $R$-module $\implies$ $eRe$ is a semisimple ring

Is every finite dimensional semisimple algebra over $k$ isomorphic to a direct sum of finitely many matrix algebras over $k$?

$R_R$ is semisimple $\implies$ $M_R$ is semisimple

End$_A(A)\cong A$

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