scholarly journals Isomorphisms of the endomorphism rings of a class of torsion-free modules

1963 ◽  
Vol 14 (4) ◽  
pp. 589-589 ◽  
Author(s):  
Kenneth G. Wolfson
Keyword(s):  
Endomorphism Rings ◽  
Free Modules ◽  
Torsion Free

scholarly journals Modules with the quasi-summand intersection property

1991 ◽  
Vol 44 (2) ◽  
pp. 189-201 ◽  
Author(s):  
Ulrich Albrecht ◽  
Jutta Hausen
Keyword(s):  
Abelian Group ◽  
Endomorphism Ring ◽  
Free Abelian Group ◽  
Intersection Property ◽  
Endomorphism Rings ◽  
Torsion Free Abelian Group ◽  
Free Abelian Groups ◽  
Free Modules ◽  
Torsion Free ◽  
Complete Characterisation

Given a torsion-free abelian group G, a subgroup A of G is said to be a quasi-summand of G if nG ≤ A ⊕ B ≤ G for some subgroup B of G and some positive integer n. If the intersection of any two quasi-summands of G is a quasi-summand, then G is said to have the quasi-summand intersection property. This is a generalisation of the summand intersection property of L. Fuchs. In this note, we give a complete characterisation of the torsion-free abelian groups (in fact, torsion-free modules over torsion-free rings) with the quasi-summand intersection property. It is shown that such a characterisation cannot be given via endomorphism rings alone but must involve the way in which the endomorphism ring acts on the underlying group. For torsion-free groups G of finite rank without proper fully invariant quasi-summands however, the structure of its quasi-endomorphism ring QE(G) suffices: G has the quasi-summand intersection property if and only if the ring QE(G) is simple or else G is strongly indecomposable.

Torsion and Torsion free Modules

2017 ◽  
pp. 219-233
Author(s):  
Jonathan S. Golan ◽  
Tom Head
Keyword(s):  
Free Modules ◽  
Torsion Free
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