臺灣博碩士論文加值系統

1.質環上具有導算的子環
假定R是一個非交換且特徵數不為2的質環, 且d是R上的非零導算.並假定U是不在中心的Lie理想且U^{d}亦不在中心. 若d是一個外導算, 則由{[d(x),x];x屬於U}生成的子環包含一個非零的理想但必須排除R滿足S_4.
2.半質環上的喬登廣義導算
假定R是一個特徵數不為2的半質環, 則R上的每個喬登廣義導算都是廣義導算.

1. On certain subrings of prime rings with derivations
Let R be a noncommutative prime ring with nonzero derivation d. U is a noncentral Lie ideal of R and U^{d} is not contained in Z. If d is outer, then the subring of R generated by {[d(x),x] ;x belong to U} contains a nonzero ideal of R except charR=2 and R satisfies S_{4}.
2. Jordan generalized derivations on semiprime rings
Let R be a 2-torson free semiprime ring, then every Jordan generalized derivation on R is a generalized derivation.

Introduction
Preliminaries
ChapterⅠ. On certain subrings of prime rings with derivations
ChapterⅡ. Jordan generalized derivations on semiprime rings
References

[1] O. D. Avraamova, Lie ideals and derivations of semiprime rings. Vestnik Moskov. Univ. Ser. I Mat. Meh (Egnl. Transl. Moscow Univ. Math. Bull.) 44, (1989), 71-73
[2] J. Bergen, I.N Herstein and J. Kerr, Lie ideals and derivations of prime rings. Algebra 71 (1981) no1, 259-267.
[3] M. Bresar, Centralizing mappings and derivations in prime rings,Algebra 156 (1993), 385-394.
[4] M. Bresar and J. Vukman, On certain subrings of prime rings with derivations. Austral. Math. 54 (1993), 133-141.
[5] H. E. Bell and W. S. Martindale 3rd, Centralizing mappings of semiprime rings. Canda. Math. Bull 30 (1987), 92-101.
[6] M. Bresar, On certain pairs of functions of semiprime rings. Pro. Amer. Math. Soc. 120 (1994), 709-713.
[7] M. Bresar and J. Vukman, Jordan derivations of prime rings. Bull. Austral. Math. Soc. 37 (1988), 321-322.
[8] M. Bresar, Jordans derivations on semiprime rimgs. Pro. Amer. Math. Soc 104 (1988) no4, 1003-1006.
[9] M. A. Chebotar, On certain subrings and ideals of prime rings. First international Tainan-Moscow Algebra Workshop, Walter de Gruyter (1996), 177-180.
[10] M. A. Chebotar and P.-H Lee, On certain subrings of prime rings with derivations. Algebra 29 (2001), 3083-3087.
[11] C.-L Chung and T.-K Lee, A note on certain subgroups of prime rings with derivations. Comm Algebra, to appear.
[12] C.-L Chung. The additive subgroup generalized by a polymial. Isr. J. Math. vol 59, (1987), 98-106.
[13] I. N. Herstein, Jordan derivations of prime rings. Pro. Amer. Soc. 8, (1957), 1104-1110.
[14] I. N. Herstein, Topics in ring theory. Univ of Chicago Press, Chicago (1969).
[15] B. Havla, Generalized derivations in rings. Comm Algebra 26, (1998), 1147-1166.
[16] V. K. Kharchenko, Differential identities of semiprime rings. Algebra and Logic 18 (1979 ), 58-80.
[17] T.-K Lee, Semiprime rings with differential identities. Bull. Inst. Math. Acad. Sinca. 20 (1992), 27-38.
[18] P.-H Lee and T.-K Lee, On derivations of prime rings. Chinese J.Math 9 (1981), 107-110.
[19] Mohammad Asfraf and Nadeem-Ur-Rehman, On Jordan generalized derivations in rings. Math. J. Okayama Univ {42} (2000), 7-9.
[20] E. Posner, Derivations in prime rings. Pro. Amer. Math. Soc (1957), 1093-1100.
[21] T-L Wong, Derivations with power-central values on multilinear polynomials. Algebra Colloq {3} (1996), no4 , 369-378.
[22] T.-L Wong, On certain subgroups of semiprime rings with derivations. to appear.