Some counterexamples for infinite dimensional Lie algebras
Compositio Mathematica, Tome 36 (1978) no. 2, pp. 203-207. 
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     author = {Stevens, Gary E.},
     title = {Some counterexamples for infinite dimensional {Lie} algebras},
     journal = {Compositio Mathematica},
     pages = {203--207},
     publisher = {Sijthoff et Noordhoff International Publishers},
     volume = {36},
     number = {2},
     year = {1978},
     mrnumber = {506509},
     zbl = {0375.17009},
     language = {en},
     url = {http://archive.numdam.org/item/CM_1978__36_2_203_0/}
}
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Stevens, Gary E. Some counterexamples for infinite dimensional Lie algebras. Compositio Mathematica, Tome 36 (1978) no. 2, pp. 203-207. http://archive.numdam.org/item/CM_1978__36_2_203_0/

[1] R.K. Amayo and I.N. Stewart: Descending Chain Conditions for Lie Algebras of Prime Characteristic. University of Warwick, 1973. | Zbl

[2] C.W. Curtis: Non-commutative Extensions of Hilbert Rings. Proc. Amer. Math. Soc., 4 (1953) 945-955. | MR | Zbl

[3] G.E. Stevens: Topics in the Theory of Infinite Dimensional Lie Algebras. Ph.D. Thesis, The University of Michigan, 1974.

[4] I.N. Stewart: Lie Algebras. Lecture Notes in Mathematics, No. 127, Springer-Verlag, New York, 1970. | MR | Zbl

[5] J.S. Wilson: "Some Properties of Groups Inherited by Normal Subgroups of Finete Index." Math. Z., 114 (1970), 19-21. | MR | Zbl