2-good rings and their extensions
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1711-1723
https://doi.org/10.4134/BKMS.2013.50.5.1711
Published online September 1, 2013
Yao Wang and Yanli Ren
Nanjing University of Information Science and Technology, Nanjing Xiaozhuang University
Abstract : P. V\'amos called a ring $R$ 2-good if every element is the sum of two units. The ring of all $n\times n$ matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if $R$ is an exchange ring with Artinian primitive factors and 2 is a unit in $R$, then $R$ is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.
Keywords : unit, 2-good ring, exchange ring, Artinian primitive factor ring, extensions of rings
MSC numbers : 16S70, 16U99
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd