scholarly journals The main decomposition of finite-dimensional protori

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Wayne Lewis ◽  
Peter Loth ◽  
Adolf Mader
Keyword(s):  
Finite Dimension ◽  
Abelian Groups ◽  
Direct Products ◽  
Pontryagin Duality ◽  
Finite Dimensional ◽  
Free Abelian Groups ◽  
Main Decomposition ◽  
Canonical Type ◽  
Fundamental Theorems ◽  
Torsion Free

AbstractA 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.

scholarly journals Filial rings on direct sums and direct products of torsion-free abelian groups

2021 ◽  
Vol 22 (1) ◽  
pp. 200-212
Author(s):  
Ekaterina Igorevna Kompantseva ◽  
Thi Quynh Trang Nguyen ◽  
Varvara Aramovna Gazaryan
Keyword(s):  
Abelian Groups ◽  
Direct Products ◽  
Direct Sums ◽  
Free Abelian Groups ◽  
Torsion Free

scholarly journals Structure of Finite-Dimensional Protori

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 93
Author(s):  
Wayne Lewis
Keyword(s):  
Structure Theorem ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Compact Groups ◽  
Real Vector ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Path Component ◽  
Free Abelian Groups ◽  
Torsion Free

A Structure Theorem for Protori is derived for the category of finite-dimensional protori (compact connected abelian groups), which details the interplay between the properties of density, discreteness, torsion, and divisibility within a finite-dimensional protorus. The spectrum of resolutions for a finite-dimensional protorus are parameterized in the structure theorem by the dual category of finite rank torsion-free abelian groups. A consequence is a universal resolution for a finite-dimensional protorus, independent of a choice of a particular subgroup. A resolution is also given strictly in terms of the path component of the identity and the union of all zero-dimensional subgroups. The structure theorem is applied to show that a morphism of finite-dimensional protori lifts to a product morphism between products of periodic locally compact groups and real vector spaces.

On the square subgroups of decomposable torsion-free abelian groups of rank three

2016 ◽  
Vol 7 (4) ◽  
Author(s):  
Fysal Hasani ◽  
Fatemeh Karimi ◽  
Alireza Najafizadeh ◽  
Yousef Sadeghi
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Free Abelian Groups ◽  
Torsion Free

AbstractThe square subgroup of an abelian group

THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF RANK TWO

2006 ◽  
Vol 06 (02) ◽  
pp. 233-251 ◽  
Author(s):  
GREG HJORTH ◽  
SIMON THOMAS
Keyword(s):  
Abelian Groups ◽  
Classification Problem ◽  
Classification Problems ◽  
Borel Reducibility ◽  
Free Abelian Groups ◽  
Torsion Free

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

Near Isomorphism for a Class of Infinite Rank Torsion-Free Abelian Groups

2007 ◽  
Vol 35 (3) ◽  
pp. 1055-1072 ◽  
Author(s):  
Ekaterina Blagoveshchenskaya ◽  
Lutz Strüngmann
Keyword(s):  
Abelian Groups ◽  
Infinite Rank ◽  
Free Abelian Groups ◽  
Torsion Free
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