The Main Decomposition of Finite-Dimensional Protori

Document Type

Peer-Reviewed Article

Publication Date

2021

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.

DOI

10.1515/jgth-2020-0079

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