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kevkev1695
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We consider finitely generated modules over an artinian ringArtin algebra. Let $X$ be an indecomposable module such that the radical $\text{rad} \,X$ is a submodule of the socle $\text{soc}\,X$. What can we say about $X$? In particular, can we bound the length of $X$?

We consider finitely generated modules over an artinian ring. Let $X$ be an indecomposable module such that the radical $\text{rad} \,X$ is a submodule of the socle $\text{soc}\,X$. What can we say about $X$? In particular, can we bound the length of $X$?

We consider finitely generated modules over an Artin algebra. Let $X$ be an indecomposable module such that the radical $\text{rad} \,X$ is a submodule of the socle $\text{soc}\,X$. What can we say about $X$? In particular, can we bound the length of $X$?

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kevkev1695
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Indecomposable modules such that the radical is a submodule of the socle

We consider finitely generated modules over an artinian ring. Let $X$ be an indecomposable module such that the radical $\text{rad} \,X$ is a submodule of the socle $\text{soc}\,X$. What can we say about $X$? In particular, can we bound the length of $X$?