Generalized differential identities on prime rings and algebras

Abu Zaid Ansari; Faiza Shujat; Ahlam Fallatah; Abu Zaid Ansari; Faiza Shujat; Ahlam Fallatah

doi:10.3934/math.20231159

AIMS Mathematics

2023, Volume 8, Issue 10: 22758-22765. doi: 10.3934/math.20231159

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Generalized differential identities on prime rings and algebras

1.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Taibah University, Madinah, Saudi Arabia

Received: 15 May 2023 Revised: 16 June 2023 Accepted: 24 June 2023 Published: 17 July 2023
MSC : 16W25, 16N60, 16N80

The goal of this study is to bring out the following conclusion. Let $ R $ be a noncommutative prime ring with $ 2(m+n)! $ torsion freeness and let $ m $ and $ n $ be fixed, non-negative integers and $ d, g $ be Jordan derivations on $ R $. If $ x^{m+n}d(x)+x^mg(x)x^n\in Z(R) $ or $ d(x)x^{m+n}+x^mg(x)x^n\in Z(R) $ or $ x^{n}d(x)x^{m}+x^mg(x)x^n\in Z(R) $ then $ d = g = 0 $ follows for every $ x\in R $.
- prime ring,
- derivation,
- generalized derivation,
- differential identities,
- Banach algebra
Citation: Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah. Generalized differential identities on prime rings and algebras[J]. AIMS Mathematics, 2023, 8(10): 22758-22765. doi: 10.3934/math.20231159

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Abstract

The goal of this study is to bring out the following conclusion. Let $ R $ be a noncommutative prime ring with $ 2(m+n)! $ torsion freeness and let $ m $ and $ n $ be fixed, non-negative integers and $ d, g $ be Jordan derivations on $ R $. If $ x^{m+n}d(x)+x^mg(x)x^n\in Z(R) $ or $ d(x)x^{m+n}+x^mg(x)x^n\in Z(R) $ or $ x^{n}d(x)x^{m}+x^mg(x)x^n\in Z(R) $ then $ d = g = 0 $ follows for every $ x\in R $.

References

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