Annihilator of Generalized Derivations with Power Values in Rings and Algebras

Md Hamidur Rahaman

doi:10.36753/mathenot.631172

EN

Annihilator of Generalized Derivations with Power Values in Rings and Algebras

Abstract

Let $\mathcal{F}, \mathcal{G}$ be two generalized derivations of prime ring $\mathcal{R}$ with characteristic different from 2 with associated derivations $d_1$ and $d_2$ respectively. We use the symbols $\mathcal{C}=\mathcal{Z(U)}$ and $\mathcal{U}$ to denote the the extended centroid of $R$ and Utumi ring of quotient of $\mathcal{R}$ respectively. Let $0\neq a \in \mathcal{R}$ and $\mathcal{F}$ and $\mathcal{G}$ satisfy $a\{(\mathcal{F}(xy)+\mathcal{G}(yx))^m-[x,y]^n\}=0$ for all $x, y\in \mathcal{J}$, a nonzero ideal, where $m$ and $n$ are natural numbers. Then either $\mathcal{R}$ is commutative or there exists $c$, $b\in \mathcal{U}$ such that $\mathcal{F}$(x) = cx and $\mathcal{G}$(x) = bx for all x ∈ R.

Keywords

Semiprime rings, Generalized derivations, extended centroid

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Md Hamidur Rahaman ^*
0000-0003-1822-7863
India

Publication Date

October 15, 2020

Submission Date

October 9, 2019

Acceptance Date

May 23, 2020

Published in Issue

Year 2020 Volume: 8 Number: 2

DOI

https://doi.org/10.36753/mathenot.631172

IZ

https://izlik.org/JA36FE54ET

APA

Rahaman, M. H. (2020). Annihilator of Generalized Derivations with Power Values in Rings and Algebras. Mathematical Sciences and Applications E-Notes, 8(2), 65-70. https://doi.org/10.36753/mathenot.631172

AMA

1.Rahaman MH. Annihilator of Generalized Derivations with Power Values in Rings and Algebras. Math. Sci. Appl. E-Notes. 2020;8(2):65-70. doi:10.36753/mathenot.631172

Chicago

Rahaman, Md Hamidur. 2020. “Annihilator of Generalized Derivations With Power Values in Rings and Algebras”. Mathematical Sciences and Applications E-Notes 8 (2): 65-70. https://doi.org/10.36753/mathenot.631172.

EndNote

Rahaman MH (October 1, 2020) Annihilator of Generalized Derivations with Power Values in Rings and Algebras. Mathematical Sciences and Applications E-Notes 8 2 65–70.

IEEE

[1]M. H. Rahaman, “Annihilator of Generalized Derivations with Power Values in Rings and Algebras”, Math. Sci. Appl. E-Notes, vol. 8, no. 2, pp. 65–70, Oct. 2020, doi: 10.36753/mathenot.631172.

ISNAD

Rahaman, Md Hamidur. “Annihilator of Generalized Derivations With Power Values in Rings and Algebras”. Mathematical Sciences and Applications E-Notes 8/2 (October 1, 2020): 65-70. https://doi.org/10.36753/mathenot.631172.

JAMA

1.Rahaman MH. Annihilator of Generalized Derivations with Power Values in Rings and Algebras. Math. Sci. Appl. E-Notes. 2020;8:65–70.

MLA

Rahaman, Md Hamidur. “Annihilator of Generalized Derivations With Power Values in Rings and Algebras”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 2, Oct. 2020, pp. 65-70, doi:10.36753/mathenot.631172.

Vancouver

1.Md Hamidur Rahaman. Annihilator of Generalized Derivations with Power Values in Rings and Algebras. Math. Sci. Appl. E-Notes. 2020 Oct. 1;8(2):65-70. doi:10.36753/mathenot.631172