A note on a paper of R. A. Beaumont and R. J. Wisner on torsion–free groups
Joint Authors
Source
The Arabian Journal for Science and Engineering. Section A, Science
Issue
Vol. 32, Issue 2A (31 Jul. 2007), pp.203-204, 2 p.
Publisher
King Fahd University of Petroleum and Minerals
Publication Date
2007-07-31
Country of Publication
Saudi Arabia
No. of Pages
2
Main Subjects
Topics
Abstract AR
سوف ننشئ في هذا البحث مثالا مضادا لاستنتاج بيومونت ويزنر المقترح في عام 1959م : إذا كانت R حلقة خالية من الدوران من الرتبة الثانية ليس لها قاسم، فإن +R تتفكك على شكل جمع مباشر حيث و كذلك V ليست مجموعة خالية. أضف إلى ذلك نعالج مسألة إيجاد حلقة R ليس لها قاسم مثل +R، و تكون خالية من الدوران، متناسقة غير قابلة للتفكك و ثنائية الرتبة.
Abstract EN
In their 1959 paper, Beaumont and Wisner conjectured that if ℜ is a rank two torsion-free ring without zero-divisors, then ℜ+ decomposes as a direct sum U ⊕ V, where U ≅ V and V is not a nil group.
We construct a counter-example to this conjecture.
To further this aim, we consider the problem of finding a ring ℜ without zero-divisors such that ℜ+ is a torsion-free homogenous indecomposable group with rank equal to two.
2000 Mathematics Subject Classification 20K15
American Psychological Association (APA)
Aghdam, A. M.& Najafizadeh, A.. 2007. A note on a paper of R. A. Beaumont and R. J. Wisner on torsion–free groups. The Arabian Journal for Science and Engineering. Section A, Science،Vol. 32, no. 2A, pp.203-204.
https://search.emarefa.net/detail/BIM-345503
Modern Language Association (MLA)
Aghdam, A. M.& Najafizadeh, A.. A note on a paper of R. A. Beaumont and R. J. Wisner on torsion–free groups. The Arabian Journal for Science and Engineering. Section A, Science Vol. 32, no. 2A (Jul. 2007), pp.203-204.
https://search.emarefa.net/detail/BIM-345503
American Medical Association (AMA)
Aghdam, A. M.& Najafizadeh, A.. A note on a paper of R. A. Beaumont and R. J. Wisner on torsion–free groups. The Arabian Journal for Science and Engineering. Section A, Science. 2007. Vol. 32, no. 2A, pp.203-204.
https://search.emarefa.net/detail/BIM-345503
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 204
Record ID
BIM-345503