The subalgebra lattice of a Boolean algebra (Q912881)

This paper surveys known and unknown properties of the lattice Sub A of all subalgebras of a Boolean algebra A. The known facts about this lattice are formulated without proofs, but complete references are provided. The paper focuses on three main areas: the general structure of Sub A, complements and quasi-complements in Sub A, and the structure of chains in Sub A. The paper's central theme is the relation between the structure of A and properties of Sub A. Thirteen unsolved problems are stated, which should greatly stimulate the study of the subalgebra lattices of Boolean algebras and related algebraic structures.