# DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS

• Kim, Byung-Do (Department of Mathematics, Kangnung National University)
• Published : 2002.10.01

#### Abstract

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A \longrightarrowA such that D($\chi$)[D($\chi$),$\chi$]D($\chi$) $\in$ rad(A) for all $\chi$ A. In this case, we have D(A) ⊆ rad(A).

#### References

1. Glasnik Mathematicki v.26 no.46 A result concerning derivations in noncommutative Banach algebras J. Vukman
2. Proc. Amer. Math. Soc. v.63 no.4 Jordan derivations on semiprime rings
3. Canad. Math. Bull v.24 no.4 Semiprime rings with nilpotent derivatives L.O. Chung;J. Luh https://doi.org/10.4153/CMB-1981-064-9
4. Proc. Amer. Math. Soc. v.116 no.4 On derivations in prime rings and Banach algebras https://doi.org/10.2307/2159463
5. Annals of Math v.128 The image of a derivation is contained in the radical M.P. Thomas https://doi.org/10.2307/1971432
6. Math. Ann v.129 Derivations on commutative normed algebras I.M. Singer;J. Wermer https://doi.org/10.1007/BF01362370
7. Proc. Amer. Math. Soc. v.24 Jordan homohorphisms and derivations on semisimple Banach algebras A.M. Sinclair https://doi.org/10.2307/2036730
8. Acta Mathematical Sinica, to appear On the derivations of semiprime rings and noncommutative Banach algebras B.D. Kim https://doi.org/10.1007/s101149900020
9. Amer. J. Math. v.90 Continuity of derivations and a problem of Kaplansky B.E. Johnson;A.M. Sinclair https://doi.org/10.2307/2373290
10. Arch. Math v.63 Derivations of noncommutative Banach algebras II M. Bresar https://doi.org/10.1007/BF01196299
11. Complete Normed Algebras F.F. Bonsall;J. Duncan

#### Cited by

1. Generalized derivations on Lie ideals in prime rings vol.65, pp.1, 2015, https://doi.org/10.1007/s10587-015-0167-4
2. JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS vol.23, pp.4, 2016, https://doi.org/10.7468/jksmeb.2016.23.4.347
3. JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, I vol.28, pp.3, 2013, https://doi.org/10.4134/CKMS.2013.28.3.535
4. Engel conditions of generalized derivations on Lie ideals and left sided ideals in prime rings and Banach Algebras vol.27, pp.7-8, 2016, https://doi.org/10.1007/s13370-016-0418-z
5. An identity with generalized derivations on lie ideals, right ideals and Banach algebras vol.62, pp.2, 2012, https://doi.org/10.1007/s10587-012-0039-0
6. JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, II vol.27, pp.1, 2014, https://doi.org/10.14403/jcms.2014.27.1.65