Identities with derivations and automorphisms on semiprime rings
The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontri...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1031 |
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| _version_ | 1832547554751938560 |
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| author | Joso Vukman |
| author_facet | Joso Vukman |
| author_sort | Joso Vukman |
| collection | DOAJ |
| description | The purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved. |
| format | Article |
| id | doaj-art-1d8c93f4311a445c943fae696afcadb2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1d8c93f4311a445c943fae696afcadb22025-02-03T06:44:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-01200571031103810.1155/IJMMS.2005.1031Identities with derivations and automorphisms on semiprime ringsJoso Vukman0Department of Mathematics, Faculty of Education, University of Maribor, Koroka cesta 160, Maribor 2000, SloveniaThe purpose of this paper is to investigate identities with derivations and automorphisms on semiprime rings. A classical result of Posner states that the existence of a nonzero centralizing derivation on a prime ring forces the ring to be commutative. Mayne proved that in case there exists a nontrivial centralizing automorphism on a prime ring, then the ring is commutative. In this paper, some results related to Posner's theorem as well as to Mayne's theorem are proved.http://dx.doi.org/10.1155/IJMMS.2005.1031 |
| spellingShingle | Joso Vukman Identities with derivations and automorphisms on semiprime rings International Journal of Mathematics and Mathematical Sciences |
| title | Identities with derivations and automorphisms on semiprime rings |
| title_full | Identities with derivations and automorphisms on semiprime rings |
| title_fullStr | Identities with derivations and automorphisms on semiprime rings |
| title_full_unstemmed | Identities with derivations and automorphisms on semiprime rings |
| title_short | Identities with derivations and automorphisms on semiprime rings |
| title_sort | identities with derivations and automorphisms on semiprime rings |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1031 |
| work_keys_str_mv | AT josovukman identitieswithderivationsandautomorphismsonsemiprimerings |