In this paper, the concept of e− CNZ rings is introduced as a generalization of symmetric rings and a particular case of e− reversible rings. Regarding the question of how idempotent elements affect CNZ property of rings. In this note, we show that e− CNZ is not left-right symmetric. We present examples of right e− CNZ rings that are not CNZ and basic properties of right e− CNZ are provided. Some subrings of matrix rings and some extensions of rings such as Jordan extension are investigated in terms of right e− CNZ.
Extensions of Nil-Reversible Rings with an Endomorphism 𝛼
2022-03
General Letters in Mathematics (GLM) (Issue : 1) (Volume : 12)
The concept of an 𝛼 − nil reversible ring is a generalization of 𝛼 − reversible ring as well as an extension of nil reversible
rings. We first consider basic properties of 𝛼 − nil reversible rings. Then we investigate extensions of 𝛼 − nil reversible, including
trivial extension, Dorroh extension and Jordan extension.
