On Gelfand residuated lattices

In this paper, a combination of algebraic and topological methods is applied to obtain new structural results on Gelfand residuated lattices. It demonstrated that Gelfand’s lattices strongly tied up with the hull–kernel topology. Particularly, it shown lattice if only its prime spectrum, equipped topology, normal. The class soft introduced, semisimple. are characterized using pure part filters. relation between filters radicals in described. spectrum homeomorphic usual maximal spectrum. characterized. Finally, proved $$\mathscr {D}$$ -topology coincide set