Prime Filters and Zariski Topology on Equality Algebras

In this paper, we present some characterizations of prime and maximal lters. moreover, we introducecap-irreducible filters of an equality algebra, investigate some results about them and relations betweenmaximal, prime, v-irreducible and cap-irreducible filters in equality algebra. also, we introduce spec-trum of an equality algebra and prove that the spectrum endowed with zariski topology is a compact t0 topological space and maximal spectrum (as a subspace of that) is a compact t1 topological space.