臺灣博碩士論文加值系統

本論文探討Jordan與Lie 結構在質環Prime Ring上主要特質，並整理簡述相關的古典理論。內容主要是探討質環上 Jordan和 Lie的同構---homomorphism與導算---Derivation的相關型態與結果。

We will discuss some properties of Jordan and Lie homomorphisms and derivations on prime rings. We first give some definitions and then we show some classic results .

1.INTRODUCTION AND PRELIMINARIES……3
1.1Introduction……3
1.2Preliminaries……4
2.JORDAN AND LIE HOMOMORPHISMS……6
2.1Jordan and Lie structure……6
2.2Jordan Homomorphisms……7
2.3Lie Homomorphisms……10
3.JORDAN AND LIE DERIVATIONS……15
3.1Jordan Derivations……15
3.2Lie Derivations……17
References……20

K. I. Beidar, W. S. Martindale III, and A. V. Mikhalev, Rings with Generalized Identities}, Marcel Dekker, Inc., New York-Basel-Hong Kong, 1996.M. Bresar, Commuting Traces of Biadditive Mappings, Commutitativity-Preserving Mappings and Lie Mappings, Trans. Amer. Math. Soc. no.2, 335(1993), 525-546.M. Bresar, Jordan Mappings of Semiprime Ring, Insititute of Mathematics, Physics and Mechanics, no.1, 127(1989), 218-228.M. Bresar, Jordan Derivation on Semiprime Rings, Proc. Amer. Math. Soc. 104 1956), 1003-1006.M. Bresar and J. Vukman, Jordan Derivation of Prime Ring, Bull. Austral. Math. Soc. 37(1988), 321-322.M. F. Smiley, Jordan Homomorphisms onto Prime Rings, Trans. Amer. Math. Soc. 84(1957), 426-429.I. N. Herstein, Jordan Homomorphism, Trans. Amer. Math. Soc. 81(1956), 331-351.I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chiago, III., 1969.I. N. Herstein, Jordan Derivation of Prime Ring, Trans. Amer. Math. Soc. 8(1957), 1104-1110.