대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권5호
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  • Pages.1711-1723
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  • 2013
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2012.12.11
  • 발행 : 2013.09.30
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초록

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.

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참고문헌

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피인용 문헌

  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 2017, https://doi.org/10.1142/S0219498817502218
  4. On 2-nil-good rings 2018, https://doi.org/10.1142/S0219498818501104