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Let R be a ring with left identity e and suitably-restrictedadditive torsion, and Z(R) its center. LetH : R R R ! R be asymmetric 3-additive mapping, and let h be the trace ofH . In this paperwe show that (i) if for eachx 2 R,hh(x); xin = hhhh(x); xi; xi;:;x i 2 Z(R)with n 1 xed, then h is commuting on R. Moreover,h is of the formh(x) = 0x3 + 1(x)x2 + 2(x)x + 3(x) for allx 2 R;where 0 2 Z(R), 1 : R ! R is an additive commuting mapping,2 : R ! R is the commuting trace of a bi-additive mapping and themapping 3 :R ! Z(R) is the trace of a symmetric 3-additive mapping;(ii) for eachx 2 R, eitherhh(x); xin = 0 or hhh(x); xin ; xm i = 0 withn 0; m 1 xed, then h = 0 on R, wherehy;xi denotes the productyx + xy and Z(R) is the center ofR. We also present the conditions whichimplies commutativity in rings with identity as motivated by the aboveresult.
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참고문헌 (5)
참고문헌 신청
/ 1957 / Derivations in Prime rings
/ 1995 / On derivations and commutativity in semiprime rings 23 : 3705 ~ 3713
/ 1999 / On additive maps and commutativity in rings 36 : 1 ~ 8
/ 2002 / Skew-commuting and commuting mappings in rings 64 : 136 ~ 144
/ 2004 / Commuting maps: a survey 8 (3) : 361 ~ 397
/ 1995 / On derivations and commutativity in semiprime rings 23 : 3705 ~ 3713
/ 1999 / On additive maps and commutativity in rings 36 : 1 ~ 8
/ 2002 / Skew-commuting and commuting mappings in rings 64 : 136 ~ 144
/ 2004 / Commuting maps: a survey 8 (3) : 361 ~ 397
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