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arxiv: math/0409417 · v1 · pith:C3KEPHFKnew · submitted 2004-09-21 · 🧮 math.RT · math.CT

Submodule Categories of Wild Representation Type

classification 🧮 math.RT math.CT
keywords lambdaringfactorfiniteobjectwildalgebracategories
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Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that $S(\Lambda)$ is controlled $k$-wild with a single control object $I\in S(\Lambda)$. In particular, it follows that each finite dimensional $k$-algebra can be realized as a quotient $\End(X)/\End(X)_I$ of the endomorphism ring of some object $X\in S(\Lambda)$ modulo the ideal $\End(X)_I$ of all maps which factor through a finite direct sum of copies of $I$.

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