Systems Simplicity

Alanod M. Sibih

Journal of Mathematics Research, 2021, vol. 13, issue 3, 54

Abstract: A simple system is a system who has no proper ideals. We prove that every simple system $\mathcal{J}$ have one of the following assertion- \begin{description} \item[$(1)$] $\mathcal{J}$ is $\mathfrak{h}-$irreducible. \item[$(2)$] $\mathcal{J}=\mathcal{J}_1\bigoplus\widetilde{\mathcal{J}_1}$ is the direct summation of two $\mathfrak{h}-$invariant and $\mathfrak{h}-$irreducible subsystems. \end{description}

Date: 2021
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