作为李代数的幂零理想的推广,定义了马尔策夫代数的理想,证明了对这样定义的幂零理想存在惟一的幂零根,并且研究了马尔策夫代数中的幂零理想与其标准构造(李代数)中的幂零理想之间的关系.
The concept of nilpotent ideals of Malcev algebras,which is a generalization of the concept of nilpotent ideals of Lie algebras,is defined,the existence of a nil radical is proven,and the relationship between the nilpotent ideals of Malcev algebras and that of its standard construction is examined.
[1] SAGLE A A. Malcev algebras [J]. Transactions of the American Mathematical Society 1961, 101(03).
[2] YAMAGUTI K. On the theory of Malcev algebras [J]. Kumamoto J Sci, Ser A 1963, 1(01).
[3] HOPKINS N C. Nilpotent ideals in Lie and anti-Lie triple systems [J]. Journal of Algebra 1995, 178.
[4] MEYBERG K. Lecture on algebras and triple systems [Z]. Virginia:University of Virginia 1972.
[5] Humphreys J E. Introduction to Lie algebra and representation theory [M]. Berlin-Heidelberg-New York:Springer-Verlag Press 1972.
[6] LISTER W G. A structure theory of Lie triple systems [J]. Transactions of the American Mathematical Society 1952, 72.
