Abstract: A
topology t
on a set X
is said to be non-Archimedean topology, if it has a
basis b
such that if B and are two
members of b,
then either or or In this
paper, we investigate two operations that make this
topology to become a Boolean ring. Maximal ideals of
such a ring and ultrafilters in t
as non-Archimedean topology have been investigated.
Finally, these relations have been characterized.
Keywords and phrases: non-Archimedean and complementary topologies, disjoint basis, Boolean rings, maximal ideals.
