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Dergiler / International Electronic Journal of Algebra / 2026 / Volume: 39 Issue: 39

Action of three $X$-generalized derivations in prime rings

Basudeb Dhara(Belda College)
Vincenzo De Filippis(University of Messina)
S. Kar(Jadavpur University)
Manami Bera(Jadavpur University)
Sayfa
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Yayın Tarihi
2026-01-10
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

If $$\mathcal{H}_1\bigg(\mathcal{H}_2(\omega(s_1,\ldots,s_n))\omega(s_1,\ldots,s_n)\bigg)=\mathcal{H}_3(\omega(s_1,\ldots,s_n)^2)$$ for all $s_1,\ldots,s_n\in \mathfrak{R}$, then we detail all potential configurations of the maps $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let $\mathfrak{R}$ be a prime ring of characteristic different from $2$, $\mathcal{Q}_r^m$ be its maximal right ring of quotients, $\mathcal{C}$ be its extended centroid and $\omega(s_1,\ldots,s_n)$ be a noncentral multilinear polynomial over $\mathcal{C}$.
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Temel Bulgular & Veri:Suppose that $\mathcal{H}_1$, $\mathcal{H}_2$ and $\mathcal{H}_3$ are three $X$-generalized derivations on $\mathfrak{R}$.
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Sonuç & Katkı:If $$\mathcal{H}_1\bigg(\mathcal{H}_2(\omega(s_1,\ldots,s_n))\omega(s_1,\ldots,s_n)\bigg)=\mathcal{H}_3(\omega(s_1,\ldots,s_n)^2)$$ for all $s_1,\ldots,s_n\in \mathfrak{R}$, then we detail all potential configurations of the maps $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Generalized derivation · $X$-generalized derivation · extended centroid

Abstract

Let $\mathfrak{R}$ be a prime ring of characteristic different from $2$, $\mathcal{Q}_r^m$ be its maximal right ring of quotients, $\mathcal{C}$ be its extended centroid and $\omega(s_1,\ldots,s_n)$ be a noncentral multilinear polynomial over $\mathcal{C}$. Suppose that $\mathcal{H}_1$, $\mathcal{H}_2$ and $\mathcal{H}_3$ are three $X$-generalized derivations on $\mathfrak{R}$. If $$\mathcal{H}_1\bigg(\mathcal{H}_2(\omega(s_1,\ldots,s_n))\omega(s_1,\ldots,s_n)\bigg)=\mathcal{H}_3(\omega(s_1,\ldots,s_n)^2)$$ for all $s_1,\ldots,s_n\in \mathfrak{R}$, then we detail all potential configurations of the maps $\mathcal{H}_1, \mathcal{H}_2$ and $\mathcal{H}_3$.

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Bu Makaleye Atıf Yap

Dhara, B., Filippis, V. D., Kar, S., Bera, M. (2026). Action of three $X$-generalized derivations in prime rings. International Electronic Journal of Algebra, Volume: 39 Issue: 39. https://doi.org/10.24330/ieja.1646846

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