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This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all restricted Lie algebras over algebraically closed fields of characteristic > 7, and for all Lie algebras having the one-and-a-half generation property, the conditions of modularity and semi-modularity are equivalent, but that the same is not true for all Lie algebras over a field of characteristic three. Semi-modular subalgebras of dimensions one and two are characterised over (perfect, in the case of two-dimensional subalgebras) fields of characteristic different from 2, 3

Year: 2008

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oai:eprints.lancs.ac.uk:8069

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- (1994). A generalization of Wilsonâ€™s theorem on Cartan subalgebras of simple Lie algebras,
- (2007). Generators of simple Lie algebras in arbitrary characteristics, preprint: arXiv:0708.1711
- (1986). Lie algebras with modular lattices of subalgebras,
- (1987). Modular rule and relative complements in the lattice of subalgebras of a Lie algebra,
- (1990). On modular subalgebras in Lie algebras of prime characteristic,
- (1988). On the existence of ad-nilpotent elements and simple Lie algebras with a subalgebra of codimension one,
- (1987). On the generators of a semisimple Lie algebra (Spanish),
- (1976). Quasi-ideals of Lie algebras,
- (1984). Rank one Lie algebras,
- (1986). Semi-modular subalgebras of a Lie algebra,
- (1993). subalgebras, quasi-ideals and inner ideals in Lie algebras of prime characteristic,
- (1989). The absolute toral rank of a Lie algebra,
- (1987). The structure of cyclic Lie algebras,
- (1989). The subalgebra lattice of a supersolvable Lie algebra,
- (1998). Toral rank one simple Lie algebras of low characteristics,
- (1997). V.R.Varea, Modularity* in Lie algebras,

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