The main decomposition of finite-dimensional protori

Author:

Lewis Wayne1,Loth Peter2,Mader Adolf3

Affiliation:

1. University of Hawaii , Honolulu Community College, 874 Dillingham Blvd. , Honolulu , HI 96817 , USA

2. Department of Mathematics , Sacred Heart University , 5401 Park Avenue , Fairfield , CT 06825 , USA

3. Department of Mathematics , University of Hawaii at Manoa , 2565 McCarthy Mall , Honolulu , HI 96922 , USA

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference15 articles.

1. D. L. Armacost, The Structure of Locally Compact Abelian Groups, Monogr. Textb. Pure Appl. Math. 68, Marcel Dekker, New York, 1981.

2. R. Baer, Abelian groups without elements of finite order, Duke Math. J. 3 (1937), no. 1, 68–122.

3. L. Fuchs, Abelian Groups, Springer Monogr. Math., Springer, Cham, 2015.

4. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis. Vol. I: Structure of Topological Groups. Integration Theory, Group Representations, Grundlehren Math. Wiss. 115, Academic Press, New York, 1963.

5. K. H. Hofmann and S. A. Morris, The Structure of Compact Groups. A Primer for the Student—a Handbook for the Expert, De Gruyter Stud. Math. 25, De Gruyter, Berlin, 2013.

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