We investigate the structure of the lattice of subalgebras of an infinite Boolean algebra; in particular, we make a contribution to the question as to when such a lattice is simple. Introduction For a Boolean algebra (D, +, ° , ~, 0, 1) , the set Sub D of all subalgebras is an algebraic lattice under set inclusion with least element 2 = {0,1} and greatest element D . If A , B < D , then A A B is just A n B , and A v B is the subalgebra of D generated by A u B . One of the earliest results in

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... study of Sub D is the fact that, if D is finite, then Sub D is dually isomorphic to a finite partition lattice, the base set being At (D) , the set of all atoms of D , see [I]. Subsequently it was shown by D. Sachs that, for an arbitrary Boolean algebra D , Sub D is dually isomorphic to a sublattice of a partition lattice, and that Sub D characterizes D. Birkhoff's result cited above implies that Sub D is simple, if D is finite. In this note, the structure of Sub D is investigated further; in particular we make a contribution to the question when Sub D is simple for