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Is there a direct proof that $M_n(\mathcal k)$ is semisimple ring.

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#ring-theory #modules #noncommutative-algebra
555
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Find radical of a quiver representation

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#modules #representation-theory #quiver
236
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How to find a basis for a tricky 2x 2 matrices vector space

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#linear-algebra #abstract-algebra #matrices #vector-spaces #modules
99
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$M_R$ is finitely generated iff Every submodule of $M_R$ is finitely generated

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#modules #self-learning
125
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A proposition on exact sequence of inverse limit (Lang, Algebra, p. 165)

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#abstract-algebra #modules #abelian-groups #exact-sequence
293
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$\bf{Z}$-module homomorphism and $\bf{Q}$-module homorphism

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#abstract-algebra #ring-theory #modules
195
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Cover of a direct summand

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#modules #projective-module
32
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Minimal Frattini Extensions

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#abstract-algebra #group-theory #finite-groups #modules
271
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If a direct sum has a projective cover, must the summands have projective covers?

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#modules #homological-algebra #projective-module
40
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Quotient different modules by the same module to get the same module.

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#abstract-algebra #modules
750
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Annihilator of a quotient module

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#abstract-algebra #modules #ideals #noncommutative-algebra
537
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If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.

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#abstract-algebra #commutative-algebra #modules
130
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Definition of direct summand

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#modules
84
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Not so usual equivalence of maximal left ideal of a ring

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#abstract-algebra #ring-theory #modules #ideals
236
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Proving that P/PJ is a projective right module over R/J

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#abstract-algebra #modules #homological-algebra #projective-module

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