On some equations related to derivations in rings and Banach algebras

• Autorzy: Vukman J. , Kosi-Ulbl I.
• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to investigate additive mapping D : R -> R, where R is a (m + n +1)! and \m2 + n2 - m - n - 4mn\ -torsion free semiprime ring with the identity element, satisfying the relation 2D(xm+n+l) = (m+-n+1)(xmD(x)xn +-xnD(x)xm), for all is an element of R and some integers m > 1, n > 1, m2 + n2 - m - n - 4mn /=0.

Słowa kluczowe

EN

Banach algebra; prime ring; Jordan derivation; derivation; commuting mapping

PL

algebra Banacha; pochodne Jordana; pierścienie pierwsze; pochodne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 61--66
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Vukman J.

autor

Kosi-Ulbl I.

• Department of Mathematics University of Maribor PEF, Koroska 160 2000 Maribor, Slovenia,

Bibliografia

• [1] M. Brešar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322.
• [2] M. Brešr, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
• [3] J. Cusack, Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324.
• [4] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.
• [5] B. E. Johnson and A. M. Sinclair, Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067-1973.
• [6] E. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.
• [7] I. M. Singer and J. Wermer, Derivations on commutative normed algebras, Math. Ann. 129 (1955), 260-264.
• [8] A. M. Sinclair, Continuity of derivations on Banach algebras, Proc. Amer. Math. Soc. 20 (1969), 166-170.
• [9] M. P. Thomas, The image of a derivation is contained in the radical, Ann. Math. 28 (1988), 435-460.
• [10] J. Vukman, Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. Vol. 109 (1990), 47-52.
• [11] J. Vukman, Derivations on semiprime rings, Bull. Austral. Math. Soc. Vol. 53 (1995), 353-359.
• [12] J. Vukman, On ?+-derivations of prime and semiprime rings, Demonstratio Math. Vol. 38 (2005), 283-290.