Automorphisms and derivations in prime rings
Let R be a non-commutative ring, I a non-zero two-sided ideal of R and f a mapping on R such that f([x, y])−[x, y] is zero or invertible for every x, y ∈ I. If R is a prime ring and f a non-trivial automorphism or a non-zero derivation on R then either R = D or R = M_2(D), the ring of all 2 × 2 matr...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1999-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
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| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/393-404.pdf |
| _version_ | 1811250383454994432 |
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| author | Vincenzo De Filippis |
| author_facet | Vincenzo De Filippis |
| author_sort | Vincenzo De Filippis |
| collection | DOAJ |
| description | Let R be a non-commutative ring, I a non-zero two-sided ideal of R and f a mapping on R such that f([x, y])−[x, y] is zero or invertible for every x, y ∈ I. If R is a prime ring and f a non-trivial automorphism or a non-zero derivation on R then either R = D or R = M_2(D), the ring of all 2 × 2 matrices over D, where D is a division ring. Moreover we will examine the case when R is a semiprime ring and f a non-zero derivation of R. |
| first_indexed | 2024-04-12T16:02:56Z |
| format | Article |
| id | doaj.art-ee13f9f3c5f541f7adc176135ef0598c |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-04-12T16:02:56Z |
| publishDate | 1999-01-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-ee13f9f3c5f541f7adc176135ef0598c2022-12-22T03:26:09ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501999-01-01193393404Automorphisms and derivations in prime ringsVincenzo De Filippis0Università di MessinaLet R be a non-commutative ring, I a non-zero two-sided ideal of R and f a mapping on R such that f([x, y])−[x, y] is zero or invertible for every x, y ∈ I. If R is a prime ring and f a non-trivial automorphism or a non-zero derivation on R then either R = D or R = M_2(D), the ring of all 2 × 2 matrices over D, where D is a division ring. Moreover we will examine the case when R is a semiprime ring and f a non-zero derivation of R.https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/393-404.pdfprime and semiprime ringsderivationsdifferential identities |
| spellingShingle | Vincenzo De Filippis Automorphisms and derivations in prime rings Rendiconti di Matematica e delle Sue Applicazioni prime and semiprime rings derivations differential identities |
| title | Automorphisms and derivations in prime rings |
| title_full | Automorphisms and derivations in prime rings |
| title_fullStr | Automorphisms and derivations in prime rings |
| title_full_unstemmed | Automorphisms and derivations in prime rings |
| title_short | Automorphisms and derivations in prime rings |
| title_sort | automorphisms and derivations in prime rings |
| topic | prime and semiprime rings derivations differential identities |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1999(3)/393-404.pdf |
| work_keys_str_mv | AT vincenzodefilippis automorphismsandderivationsinprimerings |