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Jordan derivations on rings. (English) Zbl 0327.16020

Summary: I. N. Herstein has shown that every Jordan derivation on a prime ring not of characteristic 2 is a derivation. This result is extended in this paper to the case of any ring in which \(2x=0\) implies \(x=0\) and which is semiprime or which has a commutator which is not a zero divisor.

MSC:

16W10 Rings with involution; Lie, Jordan and other nonassociative structures
16W20 Automorphisms and endomorphisms
16N60 Prime and semiprime associative rings
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References:

[1] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104 – 1110. · Zbl 0216.07202
[2] I. N. Herstein, Topics in ring theory, The University of Chicago Press, Chicago, Ill.-London, 1969. · Zbl 0232.16001
[3] Nathan Jacobson, Structure of rings, American Mathematical Society, Colloquium Publications, vol. 37, American Mathematical Society, 190 Hope Street, Prov., R. I., 1956. · Zbl 0073.02002
[4] N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479 – 502. · Zbl 0039.26402
[5] Neal H. McCoy, The theory of rings, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1964. · Zbl 0273.16001
[6] A. M. Sinclair, Jordan homomorphisms and derivations on semisimple Banach algebras., Proc. Amer. Math. Soc. 24 (1970), 209 – 214. · Zbl 0175.44001
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