scholarly journals Direct products and sums of torsion-free Abelian groups

1973 ◽  
Vol 38 (2) ◽  
pp. 235-235 ◽  
Author(s):  
C. E. Murley
Keyword(s):  
Abelian Groups ◽  
Direct Products ◽  
Free Abelian Groups ◽  
Torsion Free

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 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.

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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