| Bi-Jordan $n$-Derivations on Triangular Rings: Maximal Quotient Rings and Faithful Module |
| Received:October 25, 2023 Revised:January 31, 2024 |
| Key Words:
triangular rings maximal quotient rings faithful bimodules nest algebras extremal biderivation
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| Fund Project:Supported by the Open Research Fund of Hubei Key Laboratory of Mathematical Sciences (Central China Normal University), the Natural Science Foundation of Anhui Province (Grant No.2008085QA01) and the University Natural Science Research Project of Anhui Province (Grant No.KJ2019A0107). |
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| Abstract: |
| In this paper, we mainly study the structure of bi-Jordan $n$-derivations in triangular rings under conditions of maximal quotient rings and faithful bimodules, respectively. It is shown that every bi-Jordan $n$-derivation can be decomposed into the sum of an inner biderivation and an extremal biderivation in two different conditions. As by-products, the structures of bi-Jordan $n$-derivation over upper triangular matrix rings and nest algebras are characterized, respectively, and generalize the known results. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2024.05.003 |
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