References
F. A. M. Aldosray, On Lie algebras with finiteness conditions. Hiroshima Math. J.13, 665–674 (1983).
F. A. M. Aldosray, Subideals of the join of permutable Lie algebras. J. London Math. Soc. (2)29, 63–66 (1984).
F. A. M. Aldosray, On subideals of the join of permutable Lie algebras. Arch. Math.43, 322–327 (1984).
R. K. Amayo, A construction for Lie algebras satisfying the maximal condition for subalgebras. Comp. Math.31, 31–46 (1975).
R. K.Amayo and I. N.Stewart, Infinite-dimensional Lie algebras. Leyden 1974.
C.-Y. Chao andE. L. Stitzinger, Subinvariance in solvable Lie algebras. Canad. J. Math.28, 181–185 (1976).
M. Frank, A new simple Lie algebra of characteristic three. Proc. Amer. Math. Soc.38, 43–46 (1973).
B. Hartley, Locally nilpotent ideals of a Lie algebra. Proc. Cambridge Phil. Soc.63, 257–272 (1967).
M. Honda, Lie algebras in which the join of any set of subideals is a subideal. Hiroshima Math. J.13, 349–355 (1983).
N.Jacobson, Lie algebras. New York 1962.
F. Kubo, On an infinite-dimensional Lie algebra satisfying the maximal condition for subalgebras. Hiroshima Math. J.6, 485–487 (1976).
F. Kubo, On infinite-dimensional algebras satisfying the maximal condition for subalgebras. Hiroshima Math. J.7, 287–289 (1977).
J. C. Lennox, D. Segal andS. E. Stonehewer, The lower central series of a join of subnormal subgroups. Math. Z.154, 85–89 (1977).
J. E. Roseblade andS. E. Stonehewer, Subjunctive and locally coalescent classes. J. Algebra8, 423–435 (1968).
H. Smith, On certain subgroups of a join of subnormal subgroups. Glasgow Math. J.25, 103–105 (1984).
I. N. Stewart, Finitely presented infinite-dimensional simple Lie algebras. Arch. Math.26, 504–507 (1975).
I. N. Stewart, Subideals and serial subalgebras of Lie algebras. Hiroshima Math. J.11, 493–498 (1981).
J. P.Williams, Subnormal subgroups and subideals of Lie algebras. Ph. D. Thesis, Cambridge 1982.
H.Zassenhaus, The Theory of Groups. 2nd ed. New York 1958.
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Aldosray, F.A.M., Stewart, I. Joins of ideals of subideals of Lie algebras. Arch. Math 47, 222–228 (1986). https://doi.org/10.1007/BF01191997
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DOI: https://doi.org/10.1007/BF01191997