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Nilpotency of Subrings Generated by Sets Contained in the Middle Nucleus

Year: 2026

Type: article

Abstract: :Yen and Hentzel [8] studied the nonassociative rings with the ideal generated by setscontained in two of the three nuclei. In this paper we prove that if the additive subgroup S of anonassociative ring R generated by commutators is in the middle nucleus, then (S+SR)R for all positive integers n. Also it is proved that if S+SR = S+RS and S is contained in themiddle nucleus, then the ideal of R generated by S is nilpotent if and only if the subringgenerated by S is nilpotent. We use this to prove that if R is semiprime and the subring generatedby S is nilpotent, then S = 0 and hence R is commutative.

Source: Journal of Xi'an University of Architecture & Technology

DOI: 10.5281/zenodo.18466614

Author: K. Venkata Siva Reddy, K.Madhusudhan Reddy

Institution: University of Technology and Applied Sciences - Shinas

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W7127366755

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