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Let R be a ring with left identity. Let G : R£R ! R be a symmetric biadditive mapping and g the trace of G. Let ?? : R ! R be an endomorphism and ¯ : R ! R an epimorphism. In this paper we show the following: (i) Let R be 2- torsion-free. If g is (??; ¯)-skew-commuting on R, then we have G = 0. (ii) If g is (¯; ¯)-skew -centralizing on R, then g is (¯; ¯)-commuting on R.
(iii) Let n ¸ 2. Let R be (n+1)!-torsion- free. If g is n-(??; ¯)-skew-commuting on R, then we have G = 0. (iv) Let R be 6-torsion-free. If g is 2-(??; ¯)-commuting on R, then g is (??; ¯)-commuting on R.
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참고문헌 (5)
참고문헌 신청
/ 1990 / Commuting and centralizing mappings in prime rings 109 : 47 ~ 52
/ 1995 / On derivations and commutativity in semiprime rings 23 : 3705 ~ 3713
/ 1995 / On ring epimorphisms with centralizing conditions 23 : 67 ~ 78
/ 1999 / On additive maps and commutativity in rings 36 : 1 ~ 8
/ toappear. / ,Commuting maps:a survey
/ 1995 / On derivations and commutativity in semiprime rings 23 : 3705 ~ 3713
/ 1995 / On ring epimorphisms with centralizing conditions 23 : 67 ~ 78
/ 1999 / On additive maps and commutativity in rings 36 : 1 ~ 8
/ toappear. / ,Commuting maps:a survey
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