Alternative rings with potent and nilpotent elements
*K. Madhusudhan ReddyCorresponding authorMadhu.katta@utas.edu.omDepartment of Supportive Requirements Sciences and Mathematics UnitUniversity of Technology and Applied SciencesAl-Aqur, Shinas, Sultanate of OmanView full profile → , K. Venkata Reddy Sivakvsreddy1971@gmail.comDepartment of MathematicsMasters Junior CollegeAnantapuram, Andhra Pradesh, 515001, IndiaView full profile →
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- Received:
- 01 Nov 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2804
- Pages:
- 3335–3340
Abstract
In this paper we take an alternative ring R with certain conditions on the nilpotent elements and potent elements of R. We prove if [ab, ba] is potent ∀a ∈ R\N(R), b ∈ R\N(R) then all idempotents of R are contained in the center C of R. Using this we derived if x in R\N(R) is of the form x = n + p, where n and p are nilpotent and potent, then R is commutative.
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References
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