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2-GOOD RINGS AND THEIR EXTENSIONS
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 Title & Authors
2-GOOD RINGS AND THEIR EXTENSIONS
Wang, Yao; Ren, Yanli;
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 Abstract
P. Vmos called a ring R 2-good if every element is the sum of two units. The ring of all 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
 Cited by
1.
Some New Results on Skew Triangular Matrix Rings with Constant Diagonal, Vietnam Journal of Mathematics, 2016  crossref(new windwow)
2.
A study on skew Hurwitz series rings, Ricerche di Matematica, 2016  crossref(new windwow)
3.
Study of skew inverse Laurent series rings, Journal of Algebra and Its Applications, 2016, 1750221  crossref(new windwow)
4.
On 2-nil-good rings, Journal of Algebra and Its Applications, 2017, 1850110  crossref(new windwow)
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