2-good rings and their extensions
Bull. Korean Math. Soc. 2013 Vol. 50, No. 5, 1711-1723
Printed 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
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