Sentence:  Next let L be an arbitrary semisimple Lie algebra. Then L can be written uniquely as a direct sum L_1\oplus ·s \oplus L_t of simple <WSD>ideals</WSD> (Theorem 5.2). 
Meaning of the word marked with <WSD> tags:  A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.