臺灣博碩士論文加值系統

Given a ring R with 2R=R, R^2 neq 0 and U is a Lie ideal of R.
In this thesis, we give a characterization of prime ideals in the Lie ring U.
Namely, we prove that if W is proper Lie ideal of U, then W is a prime ideal of U if and only if there exists a prime ideal P of R such that P cap U subseteq W and (W+P)/P=Z((U+P)/P).

1. Introduction 1
2. Preliminary results 2
3. Proof of Theorem 1.4 4
References 7

[1] K. I. Beidar, Lie Algebras, National Cheng-Kung University, class notes, 2002.
[2] K. I. Beidar, Ring Theory, National Cheng-Kung University, class notes, 2002.
[3] I. N. Herstein, On the Lie structure of associative ring, Journal of Algebra 14 (1970),
561ñ571.
[4] ThomasW. Hungerford, Algebra, Springer-Verlag, New York, 1974.
[5] Charles Lanski and Susan Montgomery, Lie structure of prime rings of characteristic
2. Paci c Journal of Mathematics Vol.42, No 1, (1972), 117-135.
[6] Neal H. McCoy, The Theory of Rings, Macmillan, New York, 1964.