On the Lie structure of a prime associative superalgebra (original) (raw)
In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, A, over a ring of scalars Φ with 1/2∈Φ, if L is a Lie ideal of A and W is a subalgebra of A such that [W, L]⊆ W, then either L⊆ Z or W⊆ Z. Likewise, if V is a submodule of A and [V, L]⊆ V, then either V⊆ Z or L⊆ Z or there exists an ideal of A, M, such that 0= [M,A]⊆ V. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.
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