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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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초록· 키워드
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Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer.
If R admits a generalized derivation F associated with a derivation d such that (F([x,y]))^n=[x,y] for all x, y∈ I. Then either R is commutative or n=1, d=0 and F is the identity map on R. Moreover in case R is a semiprime ring and (F([x,y]))^n=[x, y] for all x, y∈ R, then either R is commutative or n=1, d(R)⊆ Z(R), R contains a non-zero central ideal and F(x)-x ∈ Z(R) for all x∈ R.
목차
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참고문헌 (15)
참고문헌 신청
A. Giambruno / 1981 / Derivations with nilpotent values / Rend. Circ. Mat. Palermo (2) 30 (2) : 199 ~ 206
B. Hvala / 1998 / Generalized derivations in rings / Comm. Algebra 26 (4) : 1147 ~ 1166
B. Zalar / 1991 / On centralizers of semiprime rings / Comment. Math. Univ. Carolin 32 (4) : 609 ~ 614
C. L. Chuang / 1988 / GPI's having coefficients in Utumi quotient rings / Proc. Amer. Math. Soc 103 (3) : 723 ~ 728
C. Lanski / 1993 / An Engel condition with derivation / Proc. Amer. Math. Soc 118 (3) : 731 ~ 734
B. Hvala / 1998 / Generalized derivations in rings / Comm. Algebra 26 (4) : 1147 ~ 1166
B. Zalar / 1991 / On centralizers of semiprime rings / Comment. Math. Univ. Carolin 32 (4) : 609 ~ 614
C. L. Chuang / 1988 / GPI's having coefficients in Utumi quotient rings / Proc. Amer. Math. Soc 103 (3) : 723 ~ 728
C. Lanski / 1993 / An Engel condition with derivation / Proc. Amer. Math. Soc 118 (3) : 731 ~ 734
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