On the $p$-rank of torsion-free Abelian groups of finite rank
نویسندگان
چکیده
منابع مشابه
THE CLASSIFICATION PROBLEM FOR p-LOCAL TORSION-FREE ABELIAN GROUPS OF FINITE RANK
Let n ≥ 3. We prove that if p 6= q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank n are incomparable with respect to Borel reducibility.
متن کاملOn 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 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 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 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: Czechoslovak Mathematical Journal
سال: 1962
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1962.100496