Additivity of elementary maps on gamma rings
doi:10.17398/2605-5686.34.1.61
Keywords:
Elementary maps, Gamma rings, additivityAbstract
Abstract: Let M and M' be Gamma rings, respectively. We study the additivity of surjective elementary maps of M × M' . We prove that if M contains a non-trivial γ-idempotent satisfying some conditions, then they are additive.
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References
W.E. Barnes, On the Γ-rings of Nobusawa, Pacific J. Math. 18 (1966), 411 –422.
N. Nobusawa, On a generalization of the ring theory, Osaka J. Math. 1 (1964), 81 – 89.
J.C.M. Ferreira, B.L.M. Ferreira, Additivity of n-multiplicative maps on alternative rings, Comm. Algebra 44 (2016), 1557 – 1568.
B.L.M. Ferreira, J.C.M. Ferreira, H. Guzzo, Jr., Jordan triple maps of alternative algebras, JP J. Algebra Number Theory Appl. 33 (2014), 25 – 33.
B.L.M. Ferreira, H. Guzzo Jr., J.C.M. Ferreira, Additivity of Jordan elementary maps on standard rings, Algebra Discrete Math. 18 (2014), 203 – 233.
B.L.M. Ferreira, R. Nascimento, Derivable maps on alternative rings, Recen 16 (2014), 9 – 15.
B.L.M. Ferreira, J.C.M. Ferreira, H. Guzzo Jr., Jordan triple elementary maps on alternative rings, Extracta Math. 29 (2014), 1 – 18.
P. Li, F. Lu, Additivity of elementary maps on rings, Comm. Algebra 32 (2004), 3725 – 3737.
S. Kyuno, On prime gamma rings, Pacific J. Math. 75 (1978), 185 – 190.
W.S. Martindale III, When are multiplicative mappings additive?, Proc. Amer. Math. Soc. 21 (1969), 695 – 698.
