@ 1993 KtuwerAcademic Publishers. Printed in the Netherlands. Completions of Orthomodular Lattices II

Abstract. If/C is a variety of orthomodular l ttices generated by a set of orthomodular l ttices having a finite uniform upper bound om the length of their chains, then the MacNeille completion of every algebra in/C again belongs to]C. Mathematics Subject Classifications (1991). 06A10, 20BI4. Key words: Orthomodular lattices, MacNeille completion, Boolean algebra. It is often of interest o know when the fundamental operations of an ordered structure A can be extended to operations of the MacNeille completion of A, subject to certain constraints. As an important example, the MacNeille completion of a Boolean algebra B carries the structure of a Boolean algebra, which is the injective hull of B [ 10]. Other examples naturally occur; the MacNeille completion of a Heyting algebra H can be given a Heyting algebra structure xtending that of H ([2], p. 238), the MacNeiUe completion of an ortholattice L can be given an ortholattice structure xtending that of L [18], and of course, the MacNeille completion of a lattice L can be given a lattice structure xtending that of L [19]. For a variety V of algebras whose members carry a natural partial ordering, we sa