On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings
In this paper, the concept of centrally extended α,β-higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended α,β-higher derivation is an α,β-higher derivation....
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/7214864 |
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| _version_ | 1849472788347224064 |
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| author | O. H. Ezzat |
| author_facet | O. H. Ezzat |
| author_sort | O. H. Ezzat |
| collection | DOAJ |
| description | In this paper, the concept of centrally extended α,β-higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended α,β-higher derivation is an α,β-higher derivation. Some examples are given to show that our theorems’ assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated. |
| format | Article |
| id | doaj-art-da6989cb55a04e7ba62f8f7ae1d99f46 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-da6989cb55a04e7ba62f8f7ae1d99f462025-08-20T03:24:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/7214864On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in RingsO. H. Ezzat0Department of MathematicsIn this paper, the concept of centrally extended α,β-higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended α,β-higher derivation is an α,β-higher derivation. Some examples are given to show that our theorems’ assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated.http://dx.doi.org/10.1155/2024/7214864 |
| spellingShingle | O. H. Ezzat On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings International Journal of Mathematics and Mathematical Sciences |
| title | On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings |
| title_full | On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings |
| title_fullStr | On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings |
| title_full_unstemmed | On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings |
| title_short | On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings |
| title_sort | on additivity and multiplicativity of centrally extended α β higher derivations in rings |
| url | http://dx.doi.org/10.1155/2024/7214864 |
| work_keys_str_mv | AT ohezzat onadditivityandmultiplicativityofcentrallyextendedabhigherderivationsinrings |