RADICAL OF FILTERS IN RESIDUATED LATTICES

Abstract. In this paper, the notion of the radical of a lter in residuated lattices is dened and several characterizations of the radical of a lter are given. We show that if F is a positive im- plicative lter (or obstinate lter), then Rad(F) = F. We proved the extension theorem for radical of lters in residuated lattices. Also, we study the radical of lters in linearly ordered residuated lattices.