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In an earlier paper the author has proved the existence of prime ideals and prime dual ideals in a pseudocomplemented lattice (not necessarily distributive). The present paper is devoted to a study of Stone's topology on the set of prime dual ideals of a pseudocomplemented and a bicomplemented lattice. If L is the quotient lattice arising out of the congruence relation defined by a b a* = b* in a pseudocomplemented lattice L, it is proved that Stone's space of prime dual ideals of L is homeomorphic to the subspace of maximal dual ideals of L. Stone [91 has introduced a topology for the set of all prime ideals of a distributive lattice. Balachandran [31 has made an extensive study of Stone's topology of the distributive lattice and has obtained results supplementing those of Stone. The purpose of this paper is to extend some of the results of Stone and Balachandran to pseudocomplemented and bicomplemented lattices. (A lattice closed for pseudocomplements as well as quasicomplements is called a bicomplemented lattice.) In the first section we collect some known results which are used in subsequent sections. ??2 and 3 deal with Stone's topology on the set of prime dual ideals of a pseudocomplemented lattice and a bicomplemented lattice respectively. The concluding section is devoted to a study of ideals and dual ideals of the quotient lattice of a pseudocomplemented lattice with respect to a special congruence relation. It is proved that Stone's space of prime dual ideals of the quotient lattice is homeomorphic to the subspace of maximal dual ideals of the given lattice. The author is thankful to the referee for various suggestions which helped to improve the earlier version of the paper. In particular, he is indebted to the referee for pointing out that the earlier versions of some of the results were not valid. Received by the editors June 3, 1970 and, in revised form, January 11, 1971 and October 15, 1971. AMS 1969 subject classifications. Primary 0635; Secondary 0650.

Stone’s topology for pseudocomplemented and bicomplemented lattices