scholarly journals Remark on the $p$-rank of torsion free abelian groups of infinite rank

1963 ◽  
Vol 13 (1) ◽  
pp. 1-23
Author(s):  
Ladislav Procházka
Keyword(s):  
Abelian Groups ◽  
Infinite Rank ◽  
Free Abelian Groups ◽  
Torsion Free

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

scholarly journals Locally irreducible rings

1985 ◽  
Vol 32 (1) ◽  
pp. 129-145 ◽  
Author(s):  
C. Vinsonhaler ◽  
W. Wickless
Keyword(s):  
Finite Rank ◽  
Abelian Groups ◽  
Free Groups ◽  
Additive Group ◽  
Infinite Rank ◽  
Field Of Definition ◽  
Free Abelian Groups ◽  
Definition Of ◽  
Torsion Free

In the study of torsion-free abelian groups of finite rank the notions of irreducibility, field of definition and E-ring have played significant rôles. These notions are tied together in the following theorem of R. S. Pierce:THEOREM. Let R be a ring whose additive group is torsion free finite rank irreducible and let Γ be the centralizer of QR as a QE(R) module. Then Γ is the unique smallest field of definition of R. Moreover, Γ ∩ R is an E-ring, in fact, it is a maximal E-subring of R.In this paper we consider extensions of Pierce's result to the infinite rank case. This leads to the concept of local irreducibility for torsion free groups.

Direct decomposition theory under near-isomorphism for a class of infinite rank torsion-free abelian groups

2017 ◽  
Vol 20 (2) ◽  
Author(s):  
Ekaterina Blagoveshchenskaya ◽  
Lutz H. Strüngmann
Keyword(s):  
Abelian Groups ◽  
Natural Generalization ◽  
Direct Decomposition ◽  
Decomposition Theory ◽  
Infinite Rank ◽  
Free Abelian Groups ◽  
Decomposable Groups ◽  
The Right ◽  
Torsion Free

AbstractNear-isomorphism is known as the right concept for classification theorems in the theory of almost completely decomposable groups. As a natural generalization the authors extended in [

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.

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