# 2-GOOD RINGS AND THEIR EXTENSIONS

• Wang, Yao ;
• Ren, Yanli
• Published : 2013.09.30
• 41 10

#### 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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#### Cited by

1. Some New Results on Skew Triangular Matrix Rings with Constant Diagonal 2016, https://doi.org/10.1007/s10013-016-0229-4
2. A study on skew Hurwitz series rings 2016, https://doi.org/10.1007/s11587-016-0305-9
3. Study of skew inverse Laurent series rings 2016, https://doi.org/10.1142/S0219498817502218
4. On 2-nil-good rings 2017, https://doi.org/10.1142/S0219498818501104

#### Acknowledgement

Supported by : National Nature Science Foundation of China