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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
S?(R) and [d(I), a]and h commute with ?.
📌 3 Key Takeaways
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Objective & Hypothesis:Let R be a ?-prime ring with characteristic not 2, Z(R) be the center ofR, I be a nonzero ?-ideal of R, ?, ? : R -> R be two automorphisms, dbe a nonzero (?, ?)-derivation of R and h be a nonzero derivation of R.In the present paper, it is shown that (i) If d (I) ?
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Key Findings & Data:C?,?and ? commuteswith ? then R is commutative. (ii) Let ? and ? commute with ?.
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Conclusion & Impact:S?(R) and [d(I), a]and h commute with ?.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let R be a ?-prime ring with characteristic not 2, Z(R) be the center ofR, I be a nonzero ?-ideal of R, ?, ? : R -> R be two automorphisms, dbe a nonzero (?, ?)-derivation of R and h be a nonzero derivation of R.In the present paper, it is shown that (i) If d (I) ? C?,?and ? commuteswith ? then R is commutative. (ii) Let ? and ? commute with ?. Ifa ? I ? S?(R) and [d(I), a]and h commute with ?. If dh (I) ? C?,?and h (I) ? I then R is? C commutative.
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Cite This Article
AYDIN, N., TÜRKMEN, S. (2022). Some results on ?-ideal of ?-prime ring. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 5, 1147–1156. https://ajindex.com/articles/530249