DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS

Title & Authors
DERIVATIONS OF SEMIPRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS
Kim, Byung-Do;

Abstract
Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A \longrightarrowA such that D($\small{\chi}$)[D($\small{\chi}$),$\small{\chi}$]D($\small{\chi}$) $\small{\in}$ rad(A) for all $\small{\chi}$ A. In this case, we have D(A) ⊆ rad(A).
Keywords
semiprime ring;Jordan derivation;
Language
English
Cited by
1.
ON DERIVATIONS IN NONCOMMUTATIVE SEMIPRIME RINGS AND BANACH ALGEBRAS,;

대한수학회보, 2005. vol.42. 4, pp.671-678
2.
GENERALIZED DERIVATIONS IN PRIME RINGS AND NONCOMMUTATIVE BANACH ALGEBRAS,;

대한수학회보, 2008. vol.45. 4, pp.621-629
3.
Linear Derivations Satisfying a Functional Equation on Semisimple Banach Algebras,;;

Kyungpook mathematical journal, 2007. vol.47. 1, pp.119-125
4.
ON CONTINUOUS LINEAR JORDAN DERIVATIONS OF BANACH ALGEBRAS,;;

한국수학교육학회지시리즈B:순수및응용수학, 2009. vol.16. 2, pp.227-241
5.
JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, I,;

대한수학회논문집, 2013. vol.28. 3, pp.535-558
6.
JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, II,;

충청수학회지, 2014. vol.27. 1, pp.65-87
1.
Generalized derivations on Lie ideals in prime rings, Czechoslovak Mathematical Journal, 2015, 65, 1, 179
2.
JORDAN DERIVATIONS ON A LIE IDEAL OF A SEMIPRIME RING AND THEIR APPLICATIONS IN BANACH ALGEBRAS, The Pure and Applied Mathematics, 2016, 23, 4, 347
3.
JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, I, Communications of the Korean Mathematical Society, 2013, 28, 3, 535
4.
Engel conditions of generalized derivations on Lie ideals and left sided ideals in prime rings and Banach Algebras, Afrika Matematika, 2016, 27, 7-8, 1391
5.
An identity with generalized derivations on lie ideals, right ideals and Banach algebras, Czechoslovak Mathematical Journal, 2012, 62, 2, 453
6.
JORDAN DERIVATIONS ON PRIME RINGS AND THEIR APPLICATIONS IN BANACH ALGEBRAS, II, Journal of the Chungcheong Mathematical Society, 2014, 27, 1, 65
References
1.
Complete Normed Algebras, 1973.

2.
Arch. Math, 1994. vol.63. pp.56-59

3.
Proc. Amer. Math. Soc., 1988. vol.63. 4, pp.1003-1006

4.
Canad. Math. Bull, 1981. vol.24. 4, pp.415-421

5.
Amer. J. Math., 1968. vol.90. pp.1067-1073

6.
Acta Mathematical Sinica, to appear, 0000.

7.
Proc. Amer. Math. Soc., 1970. vol.24. pp.209-214

8.
Math. Ann, 1955. vol.129. pp.260-264

9.
Annals of Math, 1988. vol.128. pp.435-460

10.
Glasnik Mathematicki, 1991. vol.26. 46, pp.83-88

11.
Proc. Amer. Math. Soc., 1992. vol.116. 4, pp.877-884