Summands of finite rank torsion free abelian groups
نویسندگان
چکیده
منابع مشابه
On the complexity of the classification problem for torsion-free abelian groups of finite rank
In 1937, Baer [5] introduced the notion of the type of an element in a torsion-free abelian group and showed that this notion provided a complete invariant for the classification problem for torsion-free abelian groups of rank 1. Since then, despite the efforts of such mathematicians as Kurosh [23] and Malcev [25], no satisfactory system of complete invariants has been found for the torsion-fre...
متن کاملOn controllers of prime ideals in group algebras of torsion-free abelian groups of finite rank
Let RA be a group ring of an abelian group A and let I be an ideal of RA . We say that a subgroup B of A controls I if I = (I ∩ RB)RA. The intersection c(I) of all subgroups of A controlling I is said to be the controller of the ideal I ; c(I) is the minimal subgroup of A which controls the ideal I . The ideal I is said to be faithful if I = A ∩ (1 + I) = 1. In theorem 4 we consider some method...
متن کاملAbelian Rank of Normal Torsion-free Finite Index Subgroups of Polyhedral Groups
Suppose that P is a convex polyhedron in the hyperbolic 3-space with finite volume and P has integer ( > 1) submultiples of it as dihedral angles. We prove that if the rank of the abelianization of a normal torsion-free finite index subgroup of the polyhedral group G associated to P is one, then P has exactly one ideal vertex of type (2,2,2,2) and G has an index two subgroup which does not cont...
متن کاملBorel superrigidity and the classification problem for the torsion-free abelian groups of finite rank
In 1937, Baer solved the classification problem for the torsion-free abelian groups of rank 1. Since then, despite the efforts of many mathematicians, no satisfactory solution has been found of the classification problem for the torsion-free abelian groups of rank n ≥ 2. So it is natural to ask whether the classification problem for the higher rank groups is genuinely difficult. In this article...
متن کاملThe Classification Problem for S-local Torsion-free Abelian Groups of Finite Rank
Suppose that n ≥ 2 and that S, T are sets of primes. Then the classification problem for the S-local torsion-free abelian groups of rank n is Borel reducible to the classification problem for the T -local torsion-free abelian groups of rank n if and only if S ⊆ T .
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1974
ISSN: 0021-8693
DOI: 10.1016/0021-8693(74)90171-9