Ring endomorphisms with nil-shifting property
محورهای موضوعی : Commutative algebraC. A. K. Ahmed 1 , R. T. M. Salim 2
1 - Department of Mathematics, University of Zakho, Kurdistan Region, Iraq
2 - Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq
کلید واژه: CNZ ring&lrm, , &lrm, reversible ring&lrm, , &lrm, matrix ring&lrm, , &lrm, polynomial ring,
چکیده مقاله :
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, introducingthe 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.
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