Results 211 to 220 of about 5,618 (233)

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.
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Direct Sum Decompositions of Torsion-Free Finite Rank Groups

, 2007
T. Faticoni
semanticscholar   +2 more sources

New Examples of Indecomposable Torsion-Free Abelian Groups of Finite Rank and Rings on Them

Journal of Algebra and its Applications, 2022
R. Andruszkiewicz, M. Woronowicz
semanticscholar   +1 more source

Torsion-free Abelian Groups with Precobalanced Finite Rank Pure Subgroups

Abelian Groups, 2022
A. Giovannitti
semanticscholar   +1 more source

Irreducible representations of certain nilpotent groups of finite rank

European Journal of Mathematics
We study irreducible representations of some nilpotent groups of finite abelian total rank. The main result of the paper states that if a torsion-free minimax group G of nilpotency class 2 admits a faithful irreducible representation φ\documentclass[12pt]
A. Tushev
semanticscholar   +1 more source

Torsion-free abelian α-irreducible groups of finite rank

Communications in Algebra, 1994
If F is a free abelian group of finite rank and α is an endomorphism or an automorphism of its divisible hull, then the α‐ hull is determined, i.e. the minimal torsion-free abelian group with this endomorphism a. Torsion-free abelian groups of finite rank are called α-irreducible if their divisible hull is α-irreducible for an automorphism a.
Alexander A. Fomin, Otto mutzbauer
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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,
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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.
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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).
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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
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