Shahrood University of Technology Journal of Algebraic Systems 2345-5128 4 2 2017 01 01 RADICAL OF FILTERS IN RESIDUATED LATTICES 111 121 852 10.22044/jas.2017.852 EN S. Motamed Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran. Journal Article 2016 01 31 ‎In this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎We show that if F is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎Rad(F)=F‎. ‎We proved the extension theorem for radical of filters in residuated lattices‎. ‎Also‎, ‎we study the radical‎ ‎of filters in linearly ordered residuated lattices‎. https://jas.shahroodut.ac.ir/article_852_9a18ec2a81ec3a16def3083c7ce891e7.pdf