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J. Korean Math. Soc. 2018; 55(5): 1143-1156
Online first article March 21, 2018 Printed September 1, 2018
https://doi.org/10.4134/JKMS.j170615
Copyright © The Korean Mathematical Society.
Singular clean rings
Afshin Amini, Babak Amini, Afsaneh Nejadzadeh, Habib Sharif
Shiraz University, Shiraz University, Shiraz University, Shiraz University
In this paper, we define right singular clean rings as rings in which every element can be written as a sum of a right singular element and an idempotent. Several properties of these rings are investigated. It is shown that for a ring $R$, being singular clean is not left-right symmetric. Also the relations between (nil) clean rings and right singular clean rings are considered. Some examples of right singular clean rings have been constructed by a given one. Finally, uniquely right singular clean rings and weakly right singular clean rings are also studied.
Keywords: singular clean ring, Nil clean ring, clean ring, singular ideal
MSC numbers: 16U99, 16N40
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