Results 191 to 200 of about 594 (218)

Direct decompositions of torsion-free Abelian groups of finite rank

Journal of Soviet Mathematics, 1985
Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 132, 17-25 (Russian) (1983; Zbl 0524.20029).
openaire   +3 more sources

Totally Transitive Torsion-Free Groups of Finite p-Rank

Algebra and Logic, 2001
A torsion-free Abelian group \(A\) is a totally transitive group if any two elements \(a,b\in A\) with the characteristic condition \(\chi_A(a)\leq\chi_A(b)\) (\(\chi_A(a)=\chi_A(b)\)) are endomorphic (automorphic) conjugate elements, i.e., there is an endomorphism (automorphism) \(f\) such that \(fa=b\).
openaire   +2 more sources

On rings with finite rank torsion free additive group

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1985
The author shows that a nilpotent ring with rank n torsion-free additive group is either commutative or satisfies the identity \(x^ n=0\). This implies that when \(n=2\) the ring is commutative. He also proves the well- known result that the divisible hull of a finite rank torsion-free ring without zero-divisors is a division ring.
openaire   +2 more sources

Direct decompositions of torsion-free Abelian groups of finite rank

Journal of Soviet Mathematics, 1990
See the review in Zbl 0631.20045.
openaire   +2 more sources

On the Complexity of the Classification Problem for Torsion-Free Abelian Groups of Finite Rank

Bulletin of Symbolic Logic, 2001
In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the ...
openaire   +2 more sources

Multiplications on torsion-free groups of finite rank

Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2023
Ekaterina Igorevna Kompantseva, Askar Tuganbaev   +1 more
openaire   +1 more source

On the torsion-free ranks of finitely generated nilpotent groups and of their abelian subgroups

Journal of Group Theory, 2004
Denote by \(f(n)\) the greatest integer \(h\) such that there exists a finitely generated nilpotent group of torsion-free rank \(h\) such that the torsion-free ranks of all Abelian subgroups of this group are not greater than \(n\). The author proves that the function \(f(n)\) satisfies the inequality \(f(n)\geq\tfrac18(n^2-4)+n\). Proving this theorem,
openaire   +2 more sources

Direct decompositions of torsion-free homogeneous Abelian groups of finite rank

Lithuanian Mathematical Journal, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Categories of Mixed and Torsion-Free Finite Rank Abelian Groups

1995
In this paper “group” always means “abelian group”. For a group G let T = T(G) be the torsion part and, for a prime p, let T p = T p (G), be the p-torsion part of G.
Alexander A. Fomin, William J. Wickless
openaire   +1 more source

Soluble Groups of Type (FP)∞ have Finite Torsion-Free Rank

Bulletin of the London Mathematical Society, 1993
A group \(G\) is said to be of type \((FP)_ \infty\) over a non-zero commutative ring \(k\) if there is an exact sequence of \(ZG\)-modules \(P_ i\) of the form \(\dots \to P_ n \to \dots \to P_ 1 \to P_ 0 \to k\) with the modules \(P_ 0,P_ 1,\dots,P_ n,\dots\) finitely generated and projective. (Here \(k\) also denotes the trivial \(ZG\)-module).
openaire   +1 more source