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Results tagged with artin-ring
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user 170711
Questions about rings satisfying the descending chain condition on ideals.
6
votes
1
answer
134
views
On the finiteness of an Auslander-Reiten component
I am reading a paper called A NOTE ON THE RADICAL OF A MODULE CATEGORY by
CLAUDIA CHAIO AND SHIPING LIU. This is Theorem 2.7:
And this is part of it's proof, in which the direction (2) $\Rightarrow $ …
- 1,690
1
vote
1
answer
424
views
injective hull and projective cover of simple modules are indecomposable
Let $A$ be an Artinian algebra. Let $S$ be a simple module over $A$. Let $\pi: S \rightarrow I$ be the injective hull and $\tau: P \rightarrow S$ be the projective cover of $S$. Then $I$ and $P$ must …
- 13k