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The Auslander and Ringel-Tachikawa Theorem for submodule embeddings

2009/03/30 by Audrey Moore, Moore, Audrey
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT #msc:16G60

paper · pdf · doi:10.48550/arxiv.0903.5274

Preprint

arxiv created 2009/03/30 · arxiv updated 2009/12/01

Abstract

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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