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Generalized derivations in prime and semiprime
- Source :
- Boletim da Sociedade Paranaense de Matemática, Vol 34, Iss 2, Pp 29-34 (2016)
- Publication Year :
- 2016
- Publisher :
- Sociedade Brasileira de Matemática, 2016.
-
Abstract
- Let $R$ be a prime ring, $I$ a nonzero ideal of $R$ and $m, n$ fixed positive integers. If $R$ admits a generalized derivation $F$ associated with a nonzero derivation $d$ such that $(F([x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover we also examine the case when $R$ is a semiprime ring.
- Subjects :
- prime and semiprime rings
generalized derivations
GPIs
Mathematics
QA1-939
Subjects
Details
- Language :
- English, Portuguese
- ISSN :
- 00378712, 21751188, and 98627406
- Volume :
- 34
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Boletim da Sociedade Paranaense de Matemática
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.b30e2be98627406f9aa4413b06e99ea5
- Document Type :
- article
- Full Text :
- https://doi.org/10.5269/bspm.v34i2.21774