2-GOOD RINGS AND THEIR EXTENSIONS

Title & Authors
2-GOOD RINGS AND THEIR EXTENSIONS
Wang, Yao; Ren, Yanli;

Abstract
P. V$\small{\acute{a}}$mos called a ring R 2-good if every element is the sum of two units. The ring of all $\small{n{\times}n}$ 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;
Language
English
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2.
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3.
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