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http://dx.doi.org/10.4134/BKMS.2013.50.5.1711

2-GOOD RINGS AND THEIR EXTENSIONS  

Wang, Yao (School of Mathematics and Statistics Nanjing University of Information Science and Technology)
Ren, Yanli (School of Mathematics and Information Technology Nanjing Xiaozhuang University)
Publication Information
Bulletin of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1711-1723 More about this Journal
Abstract
P. V$\acute{a}$mos 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;
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