On Skew Centralizing Traces of Permuting n-Additive Mappings
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Let R be a ring and D : Rn → R be n-additive mapping. A map d : R → R is said to be the trace of D if d(x) = D(x, x, ...x) for all x ∈ R. Suppose that α,β are endomorphisms of R. For any a, b ∈ R, let < a,b >(α,β)= aα(b) + β(b)a. In the present paper under certain suitable torsion restrictions it is shown that D = 0 if R satisfies either < d(x), xm >(α,β)= 0, for all x 2 R or << d(x), x >(α,β), xm >(α,β)= 0, for all x ∈ R. Further, if < d(x), x >∈ Z(R), the center of R, for all x ∈ R or < d(x)x - xd(x), x >= 0, for all x ∈ R, then it is proved that d is commuting on R. Some more related results are also obtained for additive mapping on R.
Abstract
Let R be a ring and D : Rn → R be n-additive mapping. A map d : R → R is said to be the trace of D if d(x) = D(x, x, ...x) for all x ∈ R. Suppose that α,β are endomorphisms of R. For any a, b ∈ R, let < a,b >(α,β)= aα(b) + β(b)a. In the present paper under certain suitable torsion restrictions it is shown that D = 0 if R satisfies either < d(x), xm >(α,β)= 0, for all x 2 R or << d(x), x >(α,β), xm >(α,β)= 0, for all x ∈ R. Further, if < d(x), x >∈ Z(R), the center of R, for all x ∈ R or < d(x)x - xd(x), x >= 0, for all x ∈ R, then it is proved that d is commuting on R. Some more related results are also obtained for additive mapping on R.
참고문헌 (21)
- M. Ashraf, "On symmetric bi-derivations in rings", Rend. Istit. Math. Univ. Trieste, 31(1-2), pp.25~36 (1999)
- M. Ashraf., "On derivation and commutativity in prime rings", East-West J. of Math, 3(1), pp.87~91 (2001)
- M. Ashraf., "On commutativity of rings with derivation", Result. Math, 42, pp.3~8 (2002)
- H. E. Bell., "On ring epimorphisms with centralizing conditions", Chinese J. Math, 23, pp.67~78 (1995)
- H. E. Bell., "On derivations and commutativity in semiprime rings", Comm. Algebra, 23, pp.3705~3713 (1995)
- H. E. Bell., "On additive maps and commutativity in rings", Results Math, 36, pp.1~8 (1999)
- M. Bresar, "Commuting maps : a survey", Taiwanese J. Math, 3, pp.361~397 (2004)
- I. N. Herstein, "Rings with involution" (1976), University of Chicago press
- Yong-Soo Jung, "On (？？; ¯)-skew-commuting and (？？; ¯)-skew-centralizing maps in rings with left identity", 대한수학회논문집, 20(1), pp.23~34 (2005), 대한수학회
- G. Maksa, "On the trace of symmetric biderivations", C. R. Math. Rep. Acad. Sci. Canada, 9, pp.303~307 (1987)
- M. A. O zturk, "Permuting tri-derivations in prime and semi-prime rings", East. Asian. Math. J, 15, pp.105~109 (1999)
- M. A. O zturk., "On trace of symmetric bi-derivations in near rings", Ind. J. Pure Appl. Math, 17, pp.95~102 (2004)
- 박규홍, "On 4-permuting 4-derivations in Prime and Semiprime Rings", 순수 및 응용수학, 14(4), pp.271~278 (2007), 한국수학교육학회
- 박규홍, "ON PRIME AND SEMIPRIME RINGS WITH SYMMETRIC n-DERIVATIONS", 충청수학회지, 22(3), pp.451~458 (2009), 충청수학회
- K. H. Park., "Skew-commuting and commuting mappings in rings", Erratum, 70, pp.199~200 (2005)
- 정용수, "On prime and semiprime rings with permuting 3-derivations", 대한수학회보, 44(4), pp.789~794 (2007), 대한수학회
- 박규홍, "On 3-additive mappings and commutativity in certain rings", 대한수학회논문집, 22(1), pp.41~51 (2007), 대한수학회
- E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
- J. Vukman, "Symmetric bi-derivations on prime and semiprime rings", Aequationes Math, 38, pp.245~254 (1989)
- J. Vukman, "Commuting and centralizing mappings in prime rings", Proc. Amer. Math. Soc, 109, pp.47~52 (1990)
- J. Vukman, "Two results concerning symmetric bi-derivations on prime and semiprime rings", Aequationes Math, 40, pp.181~189 (1990)