We generalize the notion of (σ,τ)-derivation of Nakajima and Bresar. We define the generalized (σ,τ)-derivations, generalized Jordan (σ,τ)-derivations, and generalized Lie (σ,τ)-derivations, We study interrelations between these classes of derivations as well as their homological properties.
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- 1.Bres ar M., “On the distance of the composition of two derivations to the generalized derivations,” Glasgow Math. J., 33, 89–93 (1991).Google Scholar
- 2.Hvala B., “Generalized derivations in rings,” Comm. Algebra, 26, No. 4, 1147–1166 (1998).Google Scholar
- 3.Nakajima A., “On categorical properties of generalized derivations,” Sci. Math., 2, 345–352 (1999).Google Scholar
- 4.Nakajima A., “Generalized Jordan derivations,” in: International Conference on Ring Theory, Birkhäuser, Boston, 2000, pp. 235–243.Google Scholar
- 5.Cusack J. M., “Jordan derivations on rings,” Proc. Amer. Math. Soc., 53, 321–324 (1975).Google Scholar
- 6.Herstein I. N., “Jordan derivations of prime rings,” Proc. Amer. Math. Soc., 8, 1104–1110 (1957).Google Scholar
- 7.Herstein I. N., Topics in Ring Theory, Univ. of Chicago Press, Chicago; London (1969).Google Scholar
- 8.Bres ar M. and Vukman J., “Jordan (θ, ϕ)-derivations,” Glasnik Mat., 26, 13–17 (1991).Google Scholar
- 9.Smiley M. F., “Jordan homomorphisms onto prime rings,” Proc. Amer. Math. Soc., 8, 426–429 (1975).Google Scholar