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On the structure of Leibniz algebras whose subalgebras are ideals or core-free. (English) Zbl 07268085
Summary: An algebra $$L$$ over a field $$F$$ is said to be a Leibniz algebra (more precisely, a left Leibniz algebra) if it satisfies the Leibniz identity: $$[[a, b], c] = [a, [b, c]] - [b, [a, c]]$$ for all $$a, b, c \in L$$. Leibniz algebras are generalizations of Lie algebras. A subalgebra $$S$$ of a Leibniz algebra $$L$$ is called a core-free, if $$S$$ does not include a non-zero ideal. We study the Leibniz algebras, whose subalgebras are either ideals or core-free.
##### MSC:
 17A32 Leibniz algebras 17A60 Structure theory for nonassociative algebras 17A99 General nonassociative rings
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