List questions from semi-simple-rings

Published on 23 Feb 2026 - 9:30

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

Published on 23 Feb 2026 - 9:30

442

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

Published on 23 Feb 2026 - 9:28

258

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Relationship between idempotents in semisimple ring.

Published on 23 Feb 2026 - 9:26

56

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Simple $\mathbb{C}G$ ring

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597

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Wedderburn components of group algebra over $\mathbb R$

Published on 23 Feb 2026 - 9:30

1.6k

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

Published on 23 Feb 2026 - 9:32

266

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

Published on 23 Feb 2026 - 9:28

122

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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 23 Feb 2026 - 9:33

75

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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 23 Feb 2026 - 9:32

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

Published on 23 Feb 2026 - 9:27

236

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

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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 23 Feb 2026 - 9:34

496

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

Published on 23 Feb 2026 - 9:29

192

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End$_A(A)\cong A$

Published on 03 Apr 2026 - 2:31

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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