No Access

Local Generalized Derivations in Prime Rings with Idempotents

Yu Wang

Mathematics & Science College, Shanghai Normal University, Shanghai 200234, China

https://doi.org/10.1142/S1005386710000301Cited by:6 (Source: Crossref)

Abstract

Let R be a prime ring with a nontrivial idempotent. In this paper, we prove that if g is an additive map of R into itself such that xg(y)z = 0 for all x, y, z ∈ R with xy = yz = 0, then g is a generalized derivation. As an application of this result, we show that every local generalized derivation in a prime ring with a nontrivial idempotent is a generalized derivation.

Keywords:

AMSC: 16W20, 16N60

References

K. I. Beidar , W. S. Martindale III and A. V. Mikhalev , Rings with Generalized Identities ( Marcel Dekker , New York-Basel-Hong Kong , 1996 ) . Google Scholar
M. Brešar, Proc. Royal Soc. Edinburgh A 137, 9 (2007). Crossref, Web of Science, Google Scholar
M. Brešar and P. Šemrl, Canad. J. Math. 45, 483 (1993). Crossref, Web of Science, Google Scholar
D. Hadwin and J. W. Kerr, J. Pure Appl. Algebra 115, 231 (1997), DOI: 10.1016/S0022-4049(96)00013-8. Crossref, Web of Science, Google Scholar
D. Hadwin and J. Li, J. Math. Anal. Appl. 290, 702 (2004), DOI: 10.1016/j.jmaa.2003.10.015. Crossref, Web of Science, Google Scholar
B. Hvala, Comm. Algebra 26(4), 1147 (1998), DOI: 10.1080/00927879808826190. Crossref, Web of Science, Google Scholar
B. E. Johnson, Trans. Amer. Math. Soc. 353, 313 (2001), DOI: 10.1090/S0002-9947-00-02688-X. Crossref, Web of Science, Google Scholar
R. V. Kadison, J. Algebra 130, 494 (1990), DOI: 10.1016/0021-8693(90)90095-6. Crossref, Web of Science, Google Scholar
R. Larson and A. R. Sourour, Proc. Sympos. Pure Math. 51, 187 (1990). Google Scholar
T. K. Lee, Comm. Algebra 27, 4057 (1999), DOI: 10.1080/00927879908826682. Crossref, Web of Science, Google Scholar
T. K. Lee, Comm. Algebra 29, 4437 (2001), DOI: 10.1081/AGB-100106767. Crossref, Web of Science, Google Scholar
J. S. Lin and C. K. Liu, Taiwenese J. Math. 10, 1183 (2006). Crossref, Google Scholar
P. Šemrl, Proc. Amer. Math. Soc. 125, 2677 (1997), DOI: 10.1090/S0002-9939-97-04073-2. Crossref, Web of Science, Google Scholar
Y. Wang, Algebra Colloq. 13, 405 (2006). Link, Web of Science, Google Scholar