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arXiv · 2107.00775

Generalization of Jordan-Lie of Finite Dimensional Associative Algebras

Hasan Mohammed Ali Shlaka
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Abstract

We generalize Baranov and Shlaka's results about bar-minimal Jordan-Lie and regular inner ideals of finite dimensional associative algebras. Let A be a finite dimensional 1-perfect associative algebras A over an algebraically closed field \mathbb{F} of characteristic p\ge0 and let A' be a subalgebra of A. We prove that for any bar-minimal Jordan-Lie inner ideal B' a A', there is a bar-minimal Jordan-Lie inner ideal of A that contains B' and if B' is regular, then is a regular inner ideal of A that contains B'. We also prove that for any strict orthogonal pair (e',f') in A', there is a strict orthogonal idempotent pair (e,f) in A such that e'A'f'\subseteq eAf

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Hasan Mohammed Ali Shlaka. 2021-07-01. Generalization of Jordan-Lie of Finite Dimensional Associative Algebras. https://arxiv.org/abs/2107.00775

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