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Journal of Linear and Topological Algebra (JLTA)
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Volume Volume 08 (2019)
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Ahmed, C., Salim, R. (2019). Ring endomorphisms with nil-shifting property. Journal of Linear and Topological Algebra (JLTA), 08(03), 191-202.
C. A. K. Ahmed; R. T. M. Salim. "Ring endomorphisms with nil-shifting property". Journal of Linear and Topological Algebra (JLTA), 08, 03, 2019, 191-202.
Ahmed, C., Salim, R. (2019). 'Ring endomorphisms with nil-shifting property', Journal of Linear and Topological Algebra (JLTA), 08(03), pp. 191-202.
Ahmed, C., Salim, R. Ring endomorphisms with nil-shifting property. Journal of Linear and Topological Algebra (JLTA), 2019; 08(03): 191-202.

Ring endomorphisms with nil-shifting property

Article 5, Volume 08, Issue 03, Summer 2019, Page 191-202  XML PDF (152.83 K)
Document Type: Research Paper
Authors
C. A. K. Ahmed1; R. T. M. Salim email 2
1Department of Mathematics, University of Zakho, Kurdistan Region, Iraq
2Department of Mathematics‎, ‎Faculty of Science‎, ‎University of Zakho‎, ‎Kurdistan Region‎, ‎Iraq
Abstract
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.
Keywords
CNZ ring‎; ‎reversible ring‎; ‎matrix ring‎; ‎polynomial ring
Main Subjects
Commutative algebra
References
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