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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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