Abstract

Non-isomorphic direct decompositions of torsion-free Abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.

中文翻译：

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无挠阿贝尔群自同态环的矩阵表示

摘要

无挠阿贝尔群的非同构直接分解反映在其允许矩阵表示的自同态环分解中。描述了一种特殊类型的矩阵环可能直接分解为单边不可分解理想的直接和的集合。这导致了非交换的不同可分解环结构之间同构的组合构造。