Results 1 to 10 of about 5,618 (233)

Summands of finite rank torsion free abelian groups

Journal of Algebra, 1974
AbstractA finite rank torsion free abelian group has, up to isomorphism, only finitely many summands.
E L Lady
exaly   +3 more sources

Rings on Abelian torsion-free groups of finite rank [PDF]

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2021
In the class of reduced Abelian torsion-free groups G of finite rank, we describe TI-groups, this means that every associative ring on G is filial. If every associative multiplication on G is the zero multiplication, then G is called a nila\documentclass[
E. Kompantseva, A. Tuganbaev
semanticscholar   +3 more sources

Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank

Mediterranean Journal of Mathematics, 2022
For an Abelian group G, any homomorphism μ:G⊗G→G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin ...
E. Kompantseva, Askar Tuganbaev
semanticscholar   +3 more sources

Torsion-Free Abelian Groups of Finite Rank with Marked Bases

Journal of Mathematical Sciences, 2021
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A. Fomin
semanticscholar   +2 more sources

Centrally essential torsion-free rings of finite rank [PDF]

Beitrage Zur Algebra Und Geometrie, 2020
It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant.
O V Lyubimtsev, A A Tuganbaev, Lyubimtsev O V   +2 more
exaly   +2 more sources

On Torsion-Free Groups of Finite Rank

Canadian Journal of Mathematics, 1984
This paper deals with two conditions which, when stated, appear similar, but when applied to finitely generated solvable groups have very different effect. We first establish the notation before stating these conditions and their implications. If H is a subgroup of a group G, let denote the setWe say G has the isolator property if is a subgroup for ...
David Meier, A. Rhemtulla
semanticscholar   +2 more sources

Strongly homogeneous torsion free abelian groups of finite rank [PDF]

Proceedings of the American Mathematical Society, 1976
An abelian group is strongly homogeneous if for any two pure rank 1 subgroups there is an automorphism sending one onto the other. Finite rank torsion free strongly homogeneous groups are characterized as the tensor product of certain subrings of algebraic number fields with finite direct ...
D. Arnold
semanticscholar   +2 more sources

TORSION-FREE ABELIAN GROUPS OF FINITE RANK AND FIELDS OF FINITE TRANSCENDENCE DEGREE

The Journal of Symbolic Logic
Abstract Let $\operatorname {TFAb}_r$ be the class of torsion-free abelian groups of rank r, and let $\operatorname {FD}_r$ be the class of fields of characteristic $0$ and transcendence degree r. We compare these classes using various notions.
M. Ho, Julia Knight, Russell Miller
semanticscholar   +3 more sources

A matrix description for torsion free abelian groups of finite rank

Rendiconti del Seminario Matematico della Università di Padova, 2020
– We describe torsion free abelian groups of finite rank applying matrices with polyadic entries. This description can be considered as a modification of the classic description by A. I. Mal 0 cev.
A. Fomin
semanticscholar   +3 more sources

The classification problem for torsion-free abelian groups of finite rank [PDF]

Journal of the American Mathematical Society, 2002
We prove that for each n ≥ 1
S. Thomas
semanticscholar   +3 more sources