举例说明了非Lie的Malcev代数的次理想与理想是2个不同的概念.给出了Malcev代数的次理想的一些基本性质,证明了半单的Malcev代数的次理想均为理想;Malcev代数的幂等次理想均为理想;幂零的Malcev代数的子代数均为次理想;当Malcev代数的所有子代数均为次理想时,此Malcev代数是可解的.
Examples are introduced to show that subideals of Malcev algebras are different from their ideals. Some basic properties of Malcev algebras'subideals are given. Propositions are shown as follows: subideals of semisimple Malcev algebras are their ideals;idempotent subideals of a Malcev algebra are its ideals;subalgebras of a nilpotent Malcev algebra are its subideals;a Malcev algebra is solvable if its subalgebras are all subideals.
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