Abstract A protorus is a compact connected abelian group of finite dimension. We use a result on finite-rank torsion-free abelian groups and Pontryagin duality to considerably generalize a well-known factorization of a finite-dimensional protorus into a product of a torus and a torus free complementary factor. We also classify direct products of protori of dimension 1 by means of canonical “type” subgroups. In addition, we produce the duals of some fundamental theorems of discrete abelian groups.

中文翻译：

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有限维原形的主要分解

摘要 A protorus 是有限维的紧连通阿贝尔群。我们使用有限秩无扭转阿贝尔群和庞特里亚金对偶性的结果将众所周知的有限维原形因式分解推广为环面和无环面互补因子的乘积。我们还通过规范的“类型”子群对维度 1 的 protori 的直接积进行分类。此外，我们产生了离散阿贝尔群的一些基本定理的对偶。