### Strongly 2-good Rings

WANG Yao1, ZHOU Yun1, REN Yan-li2 *

1. 1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2. School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, China
• Received:2016-02-14 Online:2017-02-20 Published:2017-01-18

Abstract: The concept of 2-good rings is proposed. A ring R is called strongly 2-good if for any a∈R, there exist units u1, u2∈R such that a=u1+u2 and u1u2=u2u1. Some examples of strongly 2-good rings are presented and their ring extensions are investigated.

CLC Number:

• O153.3
 [1] NICHOLSON W K. Strongly clean rings and Fittings lemma[J]. Comm Algebra, 1999, 27(8):3583-3592.[2] VÁMOS P. 2-good rings[J]. Quart J Math, 2005, 56(3):417-430.[3] WANG Yao, REN Yanli. 2-good ring and their extensions[J]. Bull Korean Math Soc, 2013, 50(5):1711-1723.[4] EHRLICH G. Unit-regular rings[J]. Port Math, 1968, 27(4):209-212.[5] RAPHAEL R. Rings which are generated by their units[J]. J Algebra, 1974, 28(1):199-205.[6] FISHER J W, SNIDER R L. Rings generated by their units[J]. J Algebra, 1976, 42(2):363-368.[7] CHEN H, KÖSE H, KURTULMAZ Y. Strongly P-clean rings and matrices[J]. Inter Elect J Algebra, 2014, 15:116-131.
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