Singular clean rings
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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.
Abstract
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.
참고문헌 (10)
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