摘要
介绍了Liecolor代数的一些性质 ,如素性、半素性、非退化性等 .给出了Liecolor代数的商代数以及弱商代数的概念 ,并把Liecolor代数的素性和半素性推广到它的商代数上 .利用没有非零零化子的理想对Liecolor代数的商代数进行刻画 ,证明了 :若L是Liecolor代数Q的子代数 ,则Q是L的商代数当且仅当Q理想吸收于L .通过具体构造证明了每一个半素Liecolor代数都有极大商代数 ,并给出这个极大商代数的等价刻画 .
Some properties of Lie color algebra, such as semiprimeness, primeness and nondegeneracy are introduced. The notions of algebra of quotients and weak algeb ra of quotients of Lie color algebras are given. The semiprimeness and primeness are lifted from a Lie color algebra to its algebras of quotients. It is shown that if L is a subgroup of a Lie color algebra Q, then Q is an algebra of quot ients of L if and only if Q is ideally absorbed into L. For every semiprime Lie color algebra, a maximal algebra of quotients is const ructed.
出处
《东南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2004年第6期865-868,共4页
Journal of Southeast University：Natural Science Edition
关键词
LieColor代数
商代数
半素性
本质理想
齐次偏导子
Lie color algebras
algebras o f quotients
semiprimeness
essential ideals
homogeneous partial derivations
