The Frattini p-subalgebra of a solvable Lie p-algebra

The Frattini /7-subalgebra of a Solvable Lie

In this paper we continue our study of the Frattini p-subalgebra of a Lie />-algebra L. We show first that if L is solvable then its Frattini p-subalgebra is an ideal of L. We then consider Lie p-algebras L in which X. is nilpotent and find necessary and sufficient conditions for the Frattini p-subalgebra to be trivial. From this we deduce, in particular, that in such an algebra every ideal als...

Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings

Is P(ω) a Subalgebra?

We consider the question of whether P(ω) is a subalgebra whenever it is a quotient of a Boolean algebra by a countably generated ideal. This question was raised privately by Murray Bell. We obtain two partial answers under the open coloring axiom. Topologically our first result is that if a zerodimensional compact space has a zero-set mapping onto βN , then it has a regular closed zero-set mapp...

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

The Lie Algebra of Smooth Sections of a T-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...