Ring endomorphisms with nil-shifting property

Journal of Linear and Topological Algebra

مقاله 5، دوره 08، شماره 03، آبان 2019، صفحه 191-202   

نوع مقاله: Research Paper

نویسندگان

C. A. K. Ahmed¹؛ R. T. M. Salim^{* 2}

¹Department of Mathematics, University of Zakho, Kurdistan Region, Iraq

²Department of Mathematics‎, ‎Faculty of Science‎, ‎University of Zakho‎, ‎Kurdistan Region‎, ‎Iraq

چکیده

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,b\in R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ property of a ring as follows‎: ‎Let $R$ be a ring and $\alpha$ an endomorphism of $R$‎, ‎we say that $ R $ is right (resp.‎, ‎left) $\alpha$-nil-shifting ring if whenever $ a\alpha(b) = 0 $ (resp.‎, ‎$\alpha(a)b = 0$) for nilpotents $a,b$ in $R$‎, ‎$ b\alpha(a) = 0 $ (resp.‎, ‎$ \alpha(b)a= 0) $‎. ‎The characterization of $\alpha$-nil-shifting rings and their related properties are investigated‎.

کلیدواژه‌ها

CNZ ring‎؛ ‎reversible ring‎؛ ‎matrix ring‎؛ ‎polynomial ring

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