The Auslander and Ringel-Tachikawa Theorem for submodule embeddings

Details The Auslander and Ringel-Tachikawa Theorem for submodule embeddings The Auslander and Ringel-Tachikawa Theorem for submodule embeddings

2009-03-30

arxiv.org/abs/0903.5274v1

Mathematics

Representation Theory

Preprint

Scientific paper

Auslander and Ringel-Tachikawa have shown that for an artinian ring R of finite representation type, every R-module is the direct sum of finitely generated indecomposable R-modules. In this paper, we will adapt this result to finite representation type full subcategories of the module category of an artinian ring which are closed under subobjects and direct sums and contain all projective modules. In particular, the results in this paper hold for subspace representations of a poset, in case this subcategory is of finite representation type.

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