Two ideals of an algebra closely related to its Frattini ideal

1980 ◽  
Vol 35 (1) ◽  
pp. 112-120 ◽  
Author(s):  
David Towers
Keyword(s):  
Frattini Ideal

scholarly journals On ideally finite Lie algebras which are lower semi-modular

1985 ◽  
Vol 28 (1) ◽  
pp. 9-11 ◽  
Author(s):  
David Towers
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Subalgebras ◽  
Lower Semi ◽  
Frattini Subalgebra ◽  
Algebra Over A Field ◽  
Frattini Ideal

The purpose of this paper is twofold: first to correct the statement of Theorem 1 in [4], and secondly to consider related problems in the class of ideally finite Lie algebras.Throughout, L will denote a Lie algebra over a field K, F(L) will be its Frattini subalgebra and φ(L) its Frattini ideal. We will denote by the class of Lie algebras all of whose maximal subalgebras have codimension 1 in L. The Lie algebra with basis {u–1, u0, u1} and multiplication u–1u0 = u–1, u–1u1 = u0, u0u1 = u1 will be labelled L1(0).

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