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GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

  • BRUNO L. M. FERREIRA (a1), RUTH N. FERREIRA (a2) and HENRIQUE GUZZO (a3)

Abstract

The purpose of this note is to prove the following. Suppose $\mathfrak{R}$ is a semiprime unity ring having an idempotent element $e$ ( $e\neq 0,~e\neq 1$ ) which satisfies mild conditions. It is shown that every additive generalized Jordan derivation on $\mathfrak{R}$ is a generalized derivation.

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[1] Brešar, M., ‘Jordan derivations on semiprime rings’, Proc. Amer. Math. Soc. 104 (1988), 10031006.
[2] Călugăreanu, G., ‘A new class of semiprime rings’, Houston J. Math. 44 (2018), 2130.
[3] Herstein, I. N., ‘Jordan derivations of prime rings’, Proc. Amer. Math. Soc. 8 (1957), 11041110.
[4] Jacobson, N., Structure of Rings, American Mathematical Society Colloquium Publications, 37 (American Mathematical Society, Providence, RI, 1964).
[5] Jing, W. and Lu, S., ‘Generalized Jordan derivations on prime rings and standard operator algebras’, Taiwanese J. Math. 7 (2003), 605613.
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GENERALIZED JORDAN DERIVATIONS ON SEMIPRIME RINGS

  • BRUNO L. M. FERREIRA (a1), RUTH N. FERREIRA (a2) and HENRIQUE GUZZO (a3)

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