Submodule Categories of Wild Representation Type

Abstract

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 $I$.

13 pages

References in corpus (1)

• A Construction of Metabelian Groups

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