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Determine $Soc(R_R)$ for $R =\left(\begin{smallmatrix} K & K \\ 0 & K \end{smallmatrix}\right)$

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#abstract-algebra #proof-verification #ring-theory #modules #socle
142
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Decomposition of socle of a ring

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#abstract-algebra #ring-theory #ideals #noncommutative-algebra #socle
992
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The radical and socle series of a module and its dual

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#finite-groups #representation-theory #noncommutative-algebra #socle
85
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A $\mathfrak{sl}_2(\mathbb{C})$-module $M$ is torsion free iff $\text{soc}(M)$ is torsion-free

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#representation-theory #lie-algebras #socle
1k
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Definition of socle of a module

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#ring-theory #modules #noncommutative-algebra #socle
368
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Socle of a direct product of finite groups.

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#group-theory #finite-groups #socle
124
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Infinite socle series

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#abstract-algebra #socle
219
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Confusion over Socle

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#abstract-algebra #ring-theory #socle
280
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Socle of representations of Klein Four group over $\mathbb{F}_2$

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#finite-groups #modules #representation-theory #socle
382
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Showing the socle of a module exists and is unique

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#modules #socle
422
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Socle of submodule relative to the module

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#abstract-algebra #ring-theory #modules #socle
519
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Canonical Module and Socle of an Artinian $k$-Algebra

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#commutative-algebra #socle
112
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socle and essential extension of finitely generated mod over an artin algebra

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#representation-theory #finitely-generated #injective-module #artinian #socle
348
Views

Socle length via semisimple filtration

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#abstract-algebra #modules #socle
102
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Must $\operatorname{Soc}(R)^2 =\operatorname{Soc}(R)^3$ (for a ring $R$)?

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#abstract-algebra #ring-theory #noncommutative-algebra #socle

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